mpms 11.1 physical properties data- temperature and pressu

Manual of Petroleum Measurement Standards Chapter I I-Physical Properties Data

Section I-Temperature and Pressure Volume Correction Factors for Generalized Crude Oils, Refined Products, and Lubricating Oils

Adjunct to: ASTM D 1250-04 and IP 200/04

MAY 2004

Copyright American Petroleum Institute Reproduced by IHS under license with API

Not for ResaleNo reproduction or networking permitted without license from IHS

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Manual of Petroleum Measurement Standards Chapter I I-Physical Properties Data

Section I-Temperature and Pressure Volume Correction Factors for Generalized Crude Oils, Refined Products, and Lubricating Oils

Adjunct to: ASTM D 1250-04 and IP 200/04

May 2004



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API publications necessarily address problems of a general nature. With respect to particular circumstances, local, state, and federal laws and regulations should be reviewed. API is not undertaking to meet the duties of employers, manufacturers, or suppliers to warn and properly train and equip their employees, and others exposed, concerning health and safety risks and precautions, nor undertaking their obligations under local, state, or federal laws. Information concerning safety and health risks and proper precautions with respect to particular materials and conditions should be obtained from the employer, the manufacturer or supplier of that material, or the material safety data sheet. Nothing contained in any API publication is to be construed as granting any right, by implication or otherwise, for the manufacture, sale, or use of any method, apparatus, or product covered by letters patent. Neither should anything contained in the publication be construed as insuring anyone against liability for infringement of letters patent. Generally, API standards are reviewed and revised, reaffirmed, or withdrawn at least every five years. Sometimes a one-time extension of up to two years will be added to this review cycle. This publication will no longer be in effect five years after its publication date as an operative API standard or, where an extension has been granted, upon republication. Status of the publication can be ascertained from the API Standards department telephone (202) 682-8000. A catalog of API publications, programs and services is published annually and updated biannually by API, and available through Global Engineering Documents, 15 Inverness Way East, M / S C303B, Englewood, CO

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801 12-5776.

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Copyright O 2004 American Petroleum Institute



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FOREWORD

M I publications may be used by anyone desiring to do so. Every effort has been made by the Institute to assure the accuracy and reliability of the data contained in them; however, the Institute makes no representation, warranty, or guarantee in connection with this publication and hereby expressly disclaims any liability or responsibility for loss or damage resulting from its use or for the violation of any federal, state, or municipal regulation with which this publication may conflict. Suggested revisions are invited and should be submitted to AFT, Standards department, 1220 L Street, NW, Washington, DC 20005, [email protected].



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CONTENTS

Section 1 ~ Temperature and Pressure Volume Correction Factors for Generalized Crude Oils, Refined Products,

and Lubricating Oils .......................................................................................................

11.1.0 Implementation Guidelines ............................................................. ................................ 1

11.1.1 Introduction & History ..................................................................... ................................ 1

11.1.1.2 1952 Temperature Correction Tables ............................................ ................................ 1 11.1.1.1

11.1.1.3 1980 Temperature Correction Tables ................................. 11.1.1.4 11.1.1.5 11.1.1.6

Early Temperature and Pressure Correction Tables ...................

1981 Pressure Correction Tables ....................................................................................... ................................ 3 Changes to Previous Standards ......................................................

Customary Temperature & Pressure Correction Tables ............

........................... 11.1.2 Purpose .................................................................................................... 5 11.1.2.1 Significance ....................................................................................... ................................ 5

11.1.2.4 Classification of Liquids ................................ .................................................................. 9

11.1.2.2 Scope ................................................................. 11.1.2.3 Temperature, Pressure, and Density Limits ....................................................................

11.1.2.4.1 Crude Oil ............... ..................................

1 1.1.2.4.3 Lubricating Oils ..................................... 11.1.2.4.4 Special Applications

11.1.2.5 Application of Tables to S s.. ............................................................... 11.1.2.5.1 Waxy Crudes .......................................... ................................................................ 11

11.1.2.5.4 LNG ......................................................... ................................................................ 11 11.1.2.5.5 Ethylene and Propylene 1 1.1.2.5.6 Butadiene .................................................................................. .............................. 11

.................................................................................................. 11

1 1.1.2.5.9 Reformulated Fuels ................................................................. .............................. 12 11.1.2.5.10 MTBE .................... .................................................................................................. 12

.............................. 12 11.1.2.5.13 Gasohol ................. .................................................................................................. 13

11.1.2.5.2 Natural and Drip Gasolines

11.1.2.5.11 JP-4

11.1.3 11.1.3.1 11.1.3.2 11.1.3.3 11.1.3.4 11.1.3.5 11.1.3.6 11.1.3.7 11.1.3.8 11.1.3.9 11.1.3.10 11.1.3.11

11.1.4

11.1.5 11.1.5.1

Outline of Calculation Procedures .................................................................................... 13 Distinction Between “Standard,” “Base,” “Observed,” and “Alternate” Conditions ............................ 13

Calculation of CTL and s Standard ................................................ 15 Base Pressure in This S ................................................................ 16 Iteration Scheme to Determine Base Density from Observed Density .................................................... 16 Calculation of CTL and CPL Factors for Base Temperatures Other Than 60°F ...... 17

Calculating the Thermal Expansion Factor for Special Applications ....................................................... 18 ....................................................................................................... 19 ections ..................... ................................................................ 19

Basic Equations ............. .................................................................................................. 14

Calculation Types ........................................... ................................................................ 18

International Temperature Scale of 1990, ITS-90 ........................................................................................ 19

Summary and Precision Statement ................................................................................... 19

Implementation Procedures ~ General ......................................................................................................... 20 Method to Convert Units of Temperature, Pressure, Thermal Expansion Factor, and Density-Related Values .................................................................................................................................................................. 21



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11.1.5.2 11.1.5.3 11.1.5.4 11.1.5.5

11.1.6 11.1.6.1

11.1.6.2 11.1.6.3

11.1.7 11.1.7.1

11.1.7.2

11.1.7.3

11.1.8 11.1.8.1 11.1.8.2 11.1.8.3

11.1.8.4

11.1.8.5

11.1.8.6

11.1.8.7

11.1.8.8

11.1.8.9

11.1.8.10

11.1.8.11

11.1.8.12

11.1.8.13

11.1.8.14

11.1.8.15

11.1.8.16

11.1.8.17

11.1.8.18

11.1.8.19

Method to Calculate Thermal Expansion Factor from Density Measurements .................................. 23 Method to Convert Temperature from ITS-90 to IPTS-68 Basis ....................................................... 27 Rounding of Values ............................................................................................................................ 28 Other Implementation Considerations ................................................................................................ 30

Implementation Procedures for Customary Units (60°F and O psig Base Conditions) ....................... 30 Method to Correct a Measured Volume to Base Conditions and Density from Base Conditions to an Alternate Temperature and Pressure ................................................................................................... 30 Method to Correct Volume and Density from Observed Conditions to Customary Base Conditions46 Method to Correct Volume and Density from Observed Conditions to Alternate Conditions ........... 63

Implementation Procedures for Metric Units (15°C or 20°C and O Wa Base Conditions) ................ 80 Method to Correct a Measured Volume to Metric Base Conditions and Density from Metric Base Conditions to an Alternate Temperature and Pressure ........................................................................ 80 Method to Correct Volume and Density from Metric Observed Conditions to Metric Base Conditions ........................................................................................................................................... 92 Method to Correct Volume and Density from Observed Metric Conditions to Alternate Metric Conditions ......................................................................................................................................... 108

Use of Implementation Procedures to Generate Correction Factors in Tabular Format ................... 130 Instructions to Generate Table 5A . API Gravity Correction to 60°F for Generalized Crude Oils 132 Instructions to Generate Table 5B . API Gravity Correction to 60°F for Generalized Products ... 134 Instructions to Generate Table 5D . API Gravity Correction to 60°F for Generalized Lubricating Oils ................................................................................................................................................... 136 Instructions to Generate Tables 6A and 6B . Correction of Volume to 60°F Against API Gravity at 60°F for Generalized Crude Oils and Products ................................................................................ 138 Instructions to Generate Tables 6D . Correction of Volume to 60°F Against API Gravity at 60°F for for Generalized Lubricating Oils ................................................................................................ 141 Instructions to Generate Table 23A . Correction of Observed Specific Gravity to Specific Gravity 60/60"F for Generalized Crude Oils ................................................................................................. 143 Instructions to Generate Table 23B . Correction of Observed Specific Gravity to Specific Gravity 60/60"F for Generalized Products .................................................................................................... 145 Instructions to Generate Table 23D . Correction of Observed Specific Gravity to Specific Gravity 60/60"F for Generalized Lubricating Oils ........................................................................................ 147 Instructions to Generate Tables 24A and 24B . Correction of Volume to 60°F Against Specific Gravity 60/60"F for Generalized Crude Oils and Products .............................................................. 149 Instructions to Generate Table 24D . Correction of Volume to 60°F Against Specific Gravity 60/60"F for Generalized Lubricating Oils ........................................................................................ 152 Instructions to Generate Table 53A . Correction of Observed Density to Density at 15°C for Generalized Crude Oils .................................................................................................................... 154 Instructions to Generate Table 53B . Correction of Observed Density to Density at 15°C for Generalized Products ........................................................................................................................ 156 Instructions to Generate Table 53D . Correction of Observed Density to Density at 15°C for Generalized Lubricating Oils ............................................................................................................ 158 Instructions to Generate Tables 54A . Correction of Volume to 15°C Against Density at 15°C for Generalized Crude Oils .................................................................................................................... 160 Instructions to Generate Tables 54B . Correction of Volume to 15°C Against Density at 15°C for Generalized Products ........................................................................................................................ 162 Instructions to Generate Tables 54D . Correction of Volume to 15°C Against Density at 15°C for Generalized Lubricating Oils ............................................................................................................ 164 Instructions to Generate Tables 59A . Correction of Observed Density to Density at 20°C for Generalized Crude Oils .................................................................................................................... 166 Instructions to Generate Tables 59B . Correction of Observed Density to Density at 20°C for Generalized Products ........................................................................................................................ 168 Instructions to Generate Tables 59D . Correction of Observed Density to Density at 20°C for Generalized Lubricating Oils ............................................................................................................ 170



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11.1.8.20

11.1.8.21

11.1.8.22

11.1.8.23

11.1.8.24

11.1.8.25

11.1.8.26

Instructions to Generate Table 60A . Correction of Volume to 20°C Against Density at 20°C for Generalized Crude Oils .................................................................................................................... 172 Instructions to Generate Table 60B . Correction of Volume to 20°C Against Density at 20°C for Generalized Products ........................................................................................................................ 174 Instructions to Generate Table 60D . Correction of Volume to 20°C Against Density at 20°C for Generalized Lubricating Oils ............................................................................................................ 176 Instructions to Generate Tables 6C & 24C . Volume Correction Factors for Individual and Special Applications Volume Correction to 60°F Against Thermal Expansion Coefficients at 60°F ........... 178 Instructions to Generate Tables 54C & 60C . Volume Correction Factors for Individual and Special Applications Volume Correction to 15°C or 20°C Against Thermal Expansion Coefficients ......... 181 Instructions to Generate 1984 Chapter 1 1.2.1 Compressibility Factor Table . Compressibility Factors for Hydrocarbons Related to API Gravity and Metering Temperature ................................ 184 Instructions to Generate 1984 Chapter 1 1.2.1M Compressibility Factor Table . Compressibility Factors for Hydrocarbons Related to Density and Metering Temperature ....................................... 186

Appendix A . History & Development of the 1980 Petroleum Measurement Tables ............................................. 188 Background 188 Experimental Project ............................................................................................................................................. 188 Fluid Groups .......................................................................................................................................................... 189 Separate Representation Needed for Crude and Product Classes .......................................................................... 189 Correlation Development ...................................................................................................................................... 189 Parameter Determination and Results .................................................................................................................... 191 Development of 1980 Tables ................................................................................................................................. 192 Summary and Precision Statement ........................................................................................................................ 193 Independent Test of the Correlation ...................................................................................................................... 193 Comparison ofthe Pre-1980 and 1980 Tables ....................................................................................................... 194 Hydrometer Corrections ........................................................................................................................................ 194 Density & Relative Density ................................................................................................................................... 194 References 195

Appendix B . History & Development of the 1981 Hydrocarbon Compressibility Factors ................................... 203 Basic Mathematical Model & Uncertainty Analysis ............................................................................................. 203 References 204

Appendix C . Development of Modified CTL Equations for Base Temperatures Other Than 60" F ...................... 205

c . 1

c.2

c.3

c.4

c.5 C.5.1 C.5.2 c.5.3

C.6

Introduction ...................................................................................................................................... 205

Changing Temperature Bases ........................................................................................................... 205

Consistency of Results ...................................................................................................................... 206

Original Equations ............................................................................................................................ 206

Mathematical Conversion fiom Customary to Metric Temperature Units ....................................... 206 Conversion of Temperatures ............................................................................................................. 206 Shift of Base Temperature Value ..................................................................................................... 207 Calculation of the 60°F Thermal Expansion Factor ......................................................................... 208

Conversion to ITS-90 Temperature Scale ........................................................................................ 208

Appendix D . International Temperature Scale of 1990. ITS-90 ............................................................................ 210 Changes to the International Temperature Scale Since 1980 ................................................................................ 210 Impact on the Petroleum Measurement Tables ...................................................................................................... 211 60°F Water Density ............................................................................................................................................... 211

Appendix E - Development of Thermal Expansion Regression Equations ............................................................. 213

Appendix F . Development of Iteration Equations ................................................................................................ 217



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Newton’s Method .................................................................................................................................................. 2 17 Derivation of This Standard’s Newton’s Method Equations ................................................................................. 217 Simplification of the Temperature Derivative Term .............................................................................................. 220 Special Applications - “C’ Tables ........................................................................................................................ 221 Use of Iteration Equations to Shift 60°F Standard Density ................................................................................... 221



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SECTION 1 - VOLUME CORRECTION FACTORS FOR CRUDE OILS. REFINED PRODUCTS. & LUBE OILS 1

Chapter 11 - Physical Properties Data

Section 1 - Temperature and Pressure Volume Correction Factors for Generalized Crude Oils, Refined Products, and Lubricating Oils

11.1.0 Implementation Guidelines

This Standard (Revised Standard) is effective upon the date of publication and supersedes the previous edition of the Standard(s) (Previous Standard(s)) referenced in Appendix A of this Revised Standard. However, due to the nature of the changes in this Revised Standard, it is recognized that guidance concerning an implementation period may be needed in order to avoid disruptions within the industry and ensure proper application. As a result, it is recommended that this Revised Standard be utilized on all new applications no later than TWO YEARS after the publication date. An application for this purpose is defined as the point where the calculation is applied.

Once the Revised Standard is implemented in a particular application, the Previous Standard will no longer be used in that application.

If an existing application complies with the Previous Standard(s) then it shall be considered in compliance with this Revised Standard.

However, the use of API standards remains voluntary and the decision on when to utilize a standard is an issue that is subject to the negotiations between the parties involved in the transaction.

11.1.1 Introduction 8, History

The density and therefore the volume of hydrocarbons is sensitive to temperature and pressure. Volume Correction Factors (VCFs) are used to correct observed volumes to equivalent volumes at a standard temperature and pressure. These standard, or base, conditions serve as a way to use volumetric measures equitably in general commerce. This Standard establishes a procedure for crude oils, liquid refined products, and lubricating oils by which density measurements taken at any temperature and pressure can be corrected to an equivalent density at the base conditions. The Standard also provides a method for making a conversion to alternate base temperatures.

The volume correction factors, in their basic form, are the output of a set of equations derived from and based on empirical data relating to the volumetric change of hydrocarbons over a range of temperatures and pressures. Traditionally, the factors have been listed in a tabular format called the Petroleum Measurement Tables. In order to introduce this document and the work that serves as its foundation, a short history of these Tables is warranted.

11 .I .I .I

Correction factors to account for the thermal expansion of liquid hydrocarbons were first formally developed in 1916 by the National Bureau of Standards (United States) under Circular No. 57. These data were based on density and temperature pairs documented in the National Bureau of Standards ( N B S ) Technologic Paper No. 77. Circular No. 57 was superseded in 1924 by Circular No. C154 which in turn was superseded by a more widely known Circular C410, in 1936. By 1945 The Institute of Petroleum (IP) was publishing the Tables for Measurement of Oil in British units.

Early Temperature and Pressure Correction Tables

The compressibility standard (API Standard 1 101 , Appendix By Table 11) for hydrocarbons in the O to 90” API gravity ranges was developed in 1945 by Jacobson, et al. It was based on limited data obtained mostly on pure compounds and lubricating oil type materials. Standard 1101 was developed without the aid of a mathematical model.

11 .I .I .2 1952 Temperature Correction Tables

In 1952 the British and the American temperature correction factor tables were joined together and made available in three units of measure: US units, British (Imperial) units, and metric units. These tables were called The Petroleum Measurement Tables and were published jointly by the American Society for Testing and Materials (ASTM) and the IP. These tables are commonly referred to as the 1952 Tables, or “Blue Book Tables.”



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5

The 1952 Tables contained many sets of correction and conversion factor tables used in the measurement of hydrocarbon liquids. The tables were numbered one through fifty-eight, each dealing with a particular conversion of units, correction of density, or correction of volume. This 1952 document reflects the evolution of the correction factor tables for the correction of density or gravity to base temperature, and the correction of volume to base temperature against density at base temperature. The following shows many of the 1952 Tables which dealt with density and volume correction. These Tables were available in two volumes, US and metric versions.

API Gravity Reduction to 60°F "API 60°F

I 1952 Tables, Density and Volume Correction Tables'

7

23

24

25

33

34

53

Description

Reduction of Volume to 60°F Against API Gravity at 60°F (Abridged Table)

Reduction of Observed Specific Gravity to Specific Gravity 60/60"F

Reduction of Volume to 60°F Against Specific Gravity 60/60"F

Reduction of Volume to 60°F Against Specific Gravity 60/60"F (Abridged Table)

Specific Gravity Reduction to 60°F for Liquefied Petroleum Gases and Natural Gasoline

Reduction of Volume to 60°F Against Specific Gravity 60/60"F for Liquefied Petroleum Gases

Reduction of Observed Density to Density at 15°C

Density Base Temperature

6 I Reduction of Volume to 60°F Against API Gravity at 60°F "API 60°F

"API I 60°F

I 60°F Relative Density





I

kg/m3 I 15°C

I kg/m3 I 15°C Reduction of Volume to 15°C Against Density at I 54 I 15°C

In 1965, the American Petroleum Institute (APl) adopted these 1952 Tables.

11 .I .I .3 1980 Temperature Correction Tables

In 1974 the API started an initiative to re-confirm the temperature correction factor tables. This resulted in a major work program of density measurements made by the National Bureau of Standards under contract to the API. The effort culminated in re-writing major sections of the 1952 Tables to produce new density and volume correction tables, commonly referred to as the 1980 Tables. Refer to Appendix A for more information on this work.

The 1980 Tables separated the density and volume correction tables into two major commodity groups: crude oils and refined products. Tables were also produced for a third grouping know as "special applications." A letter designation was added to the table numbering system devised in 1952: "A" for crude oil, "B" for refined products, and "C" for special applications. The table designations established are shown in the following table.

Tables 53 and 54 were first published in 1953 by IP. 1



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Correction of Observed Density to Density at 15°C

Correction of Volume to 15°C Against Density at 15°C

I 1980 Tables, Density and Volume Correction Tables I

53A 53B kg/m3 5oc

kg/m3 5oc 54A 54B 54c

Tables for lubricating oils, the "D" tables, were developed and released in 1982. They were issued as a FORTRAN program but the API did not publish the implementation procedures. The IP published implementation procedures for the D tables in 1984 as part of their Petroleum Measurement Paper No. 2.

Since the 1980 Tables did not deal with the density range for LPGs and NGLs, the 1952 Tables remained in use for these products. This changed in October 1998 with the publication of GPA TP-25, Temperature Correction for the Volume of Light Hydrocarbons, in which the calculation for the temperature correction factor was modified. These tables carry the 23E and 24E designations.

The 1980 Tables constituted a major data collection and analysis effort. The NBS performed temperature/density measurements on a set of crude oil and refined product samples that spanned the world. (Refer to Appendix A of Base Data-1980, for more information on this work.) Most importantly, the 1980 Tables replaced the 1952printed Tables with mathematical equations. Because the equations were now the basis for the Standard, the tables could easily be incorporated into computer subroutines via implementation procedures. It is these implementation procedures which the 1980 document made the Standard, not the table of numbers themselves.

In 1980, the implementation procedures became the first attempt to provide the petroleum industry with a means to produce identical numbers on a variety of computer hardware and software configurations. Due to computer hardware and software dissimilarities and relatively low capabilities, users would frequently get different answers from the same subroutine. Therefore, before its release, the procedure was modified in order to ensure consistent answers between different computer configurations. This made the procedure very complex which, in turn, resulted in an increased risk of programming errors by users.

11 .I .I .4 1981 Pressure Correction Tables

In 198 1 , a working group of the Committee on Static Petroleum Measurement was set up to revise the compressibility tables of Standard 1101. This group performed an extensive literature search and found only three sources of compressibility information. The resulting database was broader than that used in the previous Standard and replaced the discontinued Standard 1 1 O 1 , Appendix By Table II, 0- 1 OOOAPI gravity portion. There were two versions of this 1981 Standard: Chapter 11.2.1 using customary units and Chapter 11.2.1M using metric units. Unlike the 1980 temperature correction factor tables, the compressibility table values were the Standard, not the underlying equations. Compressibility tables for LPGs and NGLs were addressed by Chapters 1 1.2.2 and 1 1.2.2M.

11 .I .I .5 Changes to Previous Standards

Between the initial issuance of the 1980 Tables and the mid-l990s, a number of needs arose within the petroleum industry and a number of enhancements occurred in computer technology. These needs and enhancements prompted several changes to be made to the Standard that are contained herein and are highlighted here:



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o

o

o

o

The 1980 Tables were based on data obtained using the International Practical Temperature Scale 1968 (IPTS-68). This has been superseded by the International Temperature Scale 1990 (ITS-90). The Standard takes this into account by correcting the input temperature values to an IPTS-68 basis before any other calculations are performed. Standard densities are also adjusted to take into account the small shifts in the associated standard temperatures.

The accepted value of the standard density of water at 60°F has changed slightly from the value used in the 1980 Standard. This new water density only affects the inter-conversion of density values with relative density and API gravity. The impact would be seen in Tables 5,6,23, and 24.

In 1988 the IP produced implementation procedures for 20°C (Tables 59 A, B and D and 60 A, B and D) by extending the procedures used for the 15°C Tables. This was in response to the needs of countries that use 20°C as their standard temperature. Although API never published these tables, they were adopted internationally as the reference document for International Standard IS0 91-2. IS0 91-2 complements IS0 91-1, the Standard for temperatures of 60°F and 15°C that is based on Volume X. This revision incorporates the 20°C tables.

Tables for lubricating oils were developed and approved as a part of the Standard but were never fully documented. Only the FORTRAN code was published by the API in Appendix A and B of the printed 5D and 6D Tables. Implementation procedures for the lubricating oil tables first appeared in the IP's Petroleum Measurement Paper No 2: Guidelines for Users of the Petroleum Measurement Tables (API Standard 2540; IP 200; ANSI/ASTM D 1250), and later in their 20°C tables. The implementation procedures are now incorporated in this Standard.

For business reasons the Tables have been extended to lower temperatures and higher densities (i.e., lower API gravities).

Real-time density measurement using density meters has become more prevalent in the industry for input into VCF calculations. These density measurements are often made at pressures greater than atmospheric. This pressure effect must be taken into account simultaneously with any temperature effect when determining the density at standard conditions. Hence, pressure and temperature corrections have been combined into one procedure.

Rounding and truncation of initial and intermediate values have been eliminated. Rounding will only be applied to the final VCF values.

The previous Standard used a format that resulted in CTL values rounded 4 or 5 decimal digits, depending upon whether the CTL value was greater than or less than one. The final VCF values will now be rounded to a consistent 5 decimal digits. The Standard also provides a mechanism to provide unrounded factors that, when combined, give the overall rounded CTPL.

Implementation procedures needed to be updated to reflect changes in computer technology. The 1980 Tables implementation procedure used integer arithmetic in order to allow all existing computer equipment to achieve consistent results. With the advent of the IEEE Standards and the predominance of 32 bit and higher level machines, this complexity of the 1980 procedure was no longer needed. This procedure now uses a double-precision floating-point math procedure.

Flow computers in the field became common for real-time measurement of petroleum fluids. These require improved convergence methods for the correction of observed density to base density. A more robust convergence scheme now accomplishes this calculation.

The range of application for the 1980 Chapter 1 1.2.1 method has been extended to be consistent with the range used here. This is so that a single pressure correction method could be used. Since the 1980 Chapter 1 1.2.1M method was not completely consistent with the 1 1.2.1 method, it has been withdrawn. The implementation procedure for the pressure correction is now the standard, not the printed table values.

When the number of decimal digits is increased and the floating-point math format used, discrepancies between the previous 60°F, 15°C and 20°C Tables become apparent. Starting from the same input density



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and temperature, each table may produce a slightly different VCF value for the same output temperature. These differences had been concealed in the 1980 Tables by the rounding and truncation procedures. This revision adopts a new procedure for calculating CTL and CPL factors for the metric tables. The procedure ensures that the results are the same as those obtained using the 60°F tables.

0 Previous editions of the printed Tables assumed that density measurements were made with a glass hydrometer. The odd-numbered printed 1980 Tables all included a hydrometer correction on the observed density. In this Standard, no glass hydrometer corrections are applied. It is assumed that any densities measured with a glass hydrometer will be corrected before applying the calculations. Methods to correct glass hydrometer readings for use in this Standard are given in M I MPMS Chapter 9.

These updates and changes are designed to make the Standard more consistent and meet industry needs. No new hydrocarbon samples or data were taken. The basic equation forms and the associated constants used to define the temperature and pressure correction factors were not changed. Ranges of density and temperature over which certain parameters apply have been slightly changed.

11 .I .I .6

This Standard incorporates both the temperature and pressure corrections into a single, unified procedure. Creating a full "three dimensional" table representation of the Standard with all possible values of temperature, pressure, and density would produce such a large number of results as to be unmanageable. This procedure is to be used in its algorithmic form.

Previous versions of this Standard had separate tables for the temperature and pressure corrections. These can still be created as specific cases of the general procedure. The 1980 temperature correction tables can be generated by setting the pressure to the base value (one atmosphere). The pressure correction tables can be generated by printing the compressibility factor at the base pressure.

Customary Temperature & Pressure Correction Tables

Detailed instructions on how to use the implementation procedures to generate the traditional tables are given in 11.1.8.

11 .I .2 Purpose

The purpose of the Petroleum Measurement Tables is to establish a standard set of temperature and pressure related corrections to volume and density based on documented test data. The procedures explained within are designed to allow users to program computer equipment to produce correction factors consistent with those produced by other users employing different computer equipment, yet following the same programming procedure.

11.1.2.1 Significance

Oil producers, carriers, refiners, and marketers use the Tables to correct petroleum densities and volumes to the base temperatures of 60°F, 15"C, or 20°C, the standard temperatures adopted internationally by the petroleum industry. The Tables provide a means for parties to make consistent and fair fiscal transactions. The Tables also provide governmental agencies with a means to equitably assess any applicable taxes and tariffs.

11 .I .2.2 Scope

This Standard provides the algorithm and implementation procedure for the correction of temperature and pressure effects on density and volume of liquid hydrocarbons which fall within the categories of crude oil, refined products, or lubricating oils; NGLs and LPGs are excluded from consideration in this Standard. The combination of density and volume correction factors for both temperature and pressure is collectively referred to in this Standard as a Volume Correction Factor (VCF). The temperature portion of this correction is termed the Correction for the effect of Temperature on Liquid (CTL). The pressure portion is termed the Correction for the effect of Pressure on Liquid (CPL).

Including the pressure correction in this Standard represents an important change from the "temperature only" 1980 Tables. However, if the pressure is one atmosphere (the standard pressure) then there is no pressure correction and this Standard will give VCF values consistent with the 1980 Tables.



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The Standard provides general procedures for the conversion of input data to a form that is consistent with the computation procedures used to generate VCF values. This section is then followed by two sets of procedures for computing volume correction factor, one set for data expressed in customary units (temperature in OF, pressure in psig), the other for the metric system of units (temperature in OC, pressure in Wa or bar). In contrast to the 1980 Tables, the metric procedures require the procedure for customary units be used first to compute density at 60°F. This value is then further corrected to give the metric output.

The procedure recognizes three distinct commodity groups: crude oil, refined products, and lubricating oils. A special application category is also provided which provides volume correction based on the input of an experimentally derived coefficient of thermal expansion.

11.1.2.3 Temperature, Pressure, and Density Limits

The limits on this Standard are defined in a mixture of terms of customary and metric units. The following table shows the defining limits and their associated units. These values are shown in bold italics. Also shown in the table are the limits converted to their equivalent units (and, in the case of the densities, other base temperatures).

Note that only the precision levels of the defining values shown in this table are correct. The other values showing converted units have been rounded to the significant digits shown; as rounded values, they may numerically fall just outside of the actual limits established by the defining values.

In 1980 the correlation for CTL was chosen so that it would be monotonic with respect to temperature (both the function and its temperature derivative). It also did not have any discontinuities over a very wide range of temperatures and densities. This does not say that the correlation is valid outside the data that was used to generate it. Due to needs of industry to accommodate commerce at temperature and density ranges well outside those originally tested, the limits of density and temperature have been extended. This extension is purely mathematical. The algorithms that correctly predict volume correction within the original test limits have simply been applied to regions beyond the original temperature and density limits.

The following figures show the range of the original data, the extensions to give the previous standards, and the current extensions for the Generalized Crude Oils, Generalized Refined Products, Generalized Lube Oils, Special Applications, and the compressibility factors. Computed values in any of these extended regions should be used with caution. Currently, there are no data in these regions to establish uncertainty.



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I

Temperature

O F

l l l l l l

300 150

50

-50 -50

I l l l l l l

Data for Crude Oil CTL Values

1980 Extension

2000 Extension

Temperature

O F

300 150

50

-50 -50

Data for Refined Product CTL Values

~ Original 1980 Data

1980 Extension

2000 Extension

DENSITY



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Temperature

OC

150

-50

OF 350 -

300 -

250 -

200 -

150 -

100 -

50 -

0 -

-50 -

Data for Lube Oil CTL Values

................................. Original 1980 Data

1980 Extension

2000 Extension

DENSITY

13001200 1100 1000 900 80 O 70 O

Temperature Data for Special

O C

150

1 1 1 O

50

OF Application CTL Values 350 i

600

Original 1980 Data

1980 Extension

2000 Extension

I I I I 230 510 530 930

Thermal ExDansion Coefficient x I O 6 ("F-l) I

1674 I I

918 954 I

414

Thermal Expansion Coefficient x I O 6 ("C-I)



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Temperature r---j Original

O F Data for CPL Values Data

o c 350 1 150

1 O0

50

O

-50

300

250

200

150

1 O0

50

O

-50 I 1984 Range

2000 Extension

-100 fio oAp:NS'TY -2 o O 20 40 60 80 100

11 .I .2.4 Classification of Liquids

This set of correlations is intended for use with petroleum fluids comprising either crude oils, refined products, or lubricating oils that are single-phase liquids under normal operating conditions. The liquid classifications listed here are typical terms used in the industry, but local nomenclature may vary. The list is illustrative and is not meant to be all-inclusive.

11 .I .2.4.1 Crude Oil

A crude oil is considered to conform to the commodity group Generalized Crude Oils if its density falls in the range between approximately -10 to 100 OAPI. Crude oils that have been stabilized for transportation or storage purposes and whose API gravities lie within that range are considered to be part of the commodity group.

11 .I .2.4.2 Refined Products

A refined product is considered to conform to the commodity group of Generalized Refined Products if the fluid falls within one of the refined product groups. The groups are defined as follows:

1. Gasoline: Motor gasoline and unfinished gasoline blending stock with a base density range between approximately 50 OAPI and 85 OAPI. This group includes substances with the commercial identification of: 0 premium gasoline 0 gasoline 0 unleaded gasoline 0 motor spirit 0 clear gasoline 0 low leadgas 0 motor gasoline 0 catalyst gas 0 alkylate 0 catalytic cracked gasoline 0 naphtha



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0 reformulated gasoline 0 aviation gasoline

2. Jet Fuels: Jet fuels, kerosene, and Stoddard solvents with a base density range between approximately 37 OAPI and 50 OAPI. This group includes substances with the commercial identification of: 0 jet fuelA 0 jet kerosene 0 aviation jet A 0 kerosene 0 aviation turbine fuel 0 Stoddard solvent 0 white kerosene

JP-2 JP-8

3. Fuel Oils: Diesel oils, heating oils and fuel oils with a base density range between approximately -10 OAPI and 37 OAPI. This group includes substances with the commercial identification of: 0 No. 6 fueloil 0 fuel oilPA 0 low sulfur fuel 0

0 fuel oil 0

0 No. 2 furnace oil 0 furnaceoil 0 auto diesel 0 gas oil 0 No. 2 burner fuel 0 diesel fuel 0 heating fuel 0 premiumdiesel

LT (low temperature) fuel oil

fuel oils LLS (light low sulfur)

Note the product descriptors are generalizations. The commercial specification ranges of some products may place their densities partly within an adjacent class (e.g., a low density diesel may lie in the jet fuel class). In such cases, the product should be allocated to the class appropriate to its density not its descriptor.

11.1.2.4.3 Lubricating Oils

- A lubricating oil is considered to conform to the commodity group Generalized Lubricating Oils if it is a base stock derived from crude oil fractions by distillation or asphalt precipitation. For the purpose of this Standard, lubricating oils have initial boiling points greater than 700°F (37OOC) and densities in the range between approximately -10 to 45OAPI.

11 .I .2.4.4 Special Applications

Liquids that are assigned the special applications category are generally relatively pure products or homogeneous mixtures with stable (unchanging) chemical composition that are derived from petroleum (or are petroleum-based with minor proportions of other constituents) and have been tested to establish a specific thermal expansion factor for the particular fluid. These tables should be considered for use when:

0 The generalized commodity groups' parameters are suspected of not adequately representing the thermal expansion properties of the liquid.

0 A precise thermal expansion coefficient can be determined by experiment. A minimum of 1 O temperature/density data points is recommended to use this method. See 1 1.1.5.2 for the procedure to calculate the thermal expansion coefficient from measured density data.



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0 Buyer and seller agree that, for their purpose, a greater degree of equity can be obtained using factors specifically measured for the liquid involved in the transaction.

11.1.2.5 Application of Tables to Specific Substances

The following are guidelines for the use of the correlations for specific products.

11 .I .2.5.1 Waxy Crudes

It is the convention in the petroleum industry to apply the Generalized Crude Oil Tables to waxy crude oils even when they are at temperatures below that at which wax forms as a separate phase. However, the density of the crude oil should be determined at a temperature at which the oil exists as a single liquid phase.

11.1.2.5.2 Natural and Drip Gasolines

Natural gasolines are paraffinic substances and are not actually refined products. These substances should be considered part of the Generalized Crude Oil commodity group provided their density lies in the appropriate range.

Drip gasoline is the paraffinic condensate from gas well production. Drip gasoline is a mixture of natural gas liquids, primarily butanes, pentanes, hexanes, and heptanes. Drip gasoline should also be considered part of the Generalized Crude Oil commodity group provided its density lies in the appropriate range.

Aromatic natural gasoline should be considered part of the Generalized Refined Products commodity group.

11.1.2.5.3 LPG and NGL

LPGs (Liquefied Petroleum Gases) and NGLs (Natural Gas Liquids) are predominantly butane and propane separated from natural gasoline or natural gas or produced during refinery processing. Most LPGs and NGLs are less dense than the liquids covered by this Standard. Gas Processors Association (GPA) Technical Publication TP- 25 Temperature Correction For ïñe Volume Of Light Hydrocarbons (or its successor) should be used for the temperature portion of the volume correction factors for liquids with 60°/600 relative densities of 0.3500 to 0.6880 (272.8 to 74.2’API). The tables in this Standard generally apply to products that do not have to be stored in pressurized containers at normal temperatures.

11 .I .2.5.4 LNG

LNG (Liquefied Natural Gas) is predominantly methane, ethane, and propane. LNG is less dense than the liquids covered by this Standard.

11 .I .2.5.5 Ethylene and Propylene

API Chapter 1 1.3.2.1 “Ethylene Density” encompasses the temperature portion of the volume correction factors. API Chapter 1 1.3.2.2 “Propylene Compressibility” encompasses the temperature portion of the volume correction factors. Use this Standard for the pressure correction portion of the volume correction factors.

11 .I .2.5.6 Butadiene

Use ASTM Standard D1550 for the temperature correction portion of the volume factors for butadiene. Use this Standard for the pressure correction portion of the volume correction factors.

11 .I .2.5.7 Cyclohexane and Aromatics

Use ASTM Standard D1555 for the temperature correction portion of the volume factors for cyclohexane and aromatic compounds. Use this Standard for the pressure correction portion of the volume correction factors.



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11 .I .2.5.8 Asphalts and Road Tars

The Asphalt Institute recommends the use of ASTM D43 1 1 for volume correction factors of asphalt and ASTM D633 for volume correction factors of road tar. The API recommends that historical Tables 6 and 7 are also acceptable.

11 .I .2.5.9 Reformulated Fuels

API has investigated volume correction factors for reformulated fuels. Included in this study were gasoline feedstocks containing any one of the following oxygenates: MTBE, ETBE, DIPE, and TAME. The addition of minor proportions of ethers to gasolines, up to 2.7 wt?? oxygen, such as permitted in many national fuels specifications, does not significantly change the correction factors from the Generalized Refined Products table.

The Special Applications procedure, which requires laboratory testing of a representative sample, was also found satisfactory for all of the gasolines, oxygenates, and mixtures studied.

11 .I .2.5.1 O MTBE

Methyl tertiary butyl ether (MTBE) is best represented by the Special Applications procedure with a 60°F thermal expansion factor of 789.0~10-~ OF-'.

11.1.2.5.11 JP-4

The NIST database contained four samples of the substance known as Jp-4. The open literature contains data on six additional samples. (An independent industrial laboratory under government contract measured these data.) The ten samples encompass a density range at 60°F of 744.3 to 786.5 kg/m3. A study of these ten samples shows that:

0 Six samples are best represented as a Generalized Crude Oil. Four samples are best represented as a Generalized Refined Product.

0 When the sample is best represented as a Generalized Refined Product, the error in representing it as a Generalized Crude Oil is very small.

0 However, when the sample is best represented as a Generalized Crude Oil, the error in representing it as a Generalized Refined Product is significant.

In consideration of these results it is recommended:

0 In the general case, represent Jp-4 as a Generalized Crude Oil.

0 In cases where the buyer and seller agree that a greater degree of precision is desirable, determine the coefficient of thermal expansion of the various blends and use the special application tables.

The above recommendations apply only to Jp-4 which is a blend. Other jet fuels such as Jp-2 and Jp-8 or materials that have densities at 60°F of 787.5 kg/m3 or greater are well represented as a Generalized Refined Product.

11 .I .2.5.12 Pure Compounds

Pure paraffinic compounds (C5+) are well represented as Generalized Crude Oils within the range of the correlations. Non-paraffinic pure compounds (C5+) are not well represented as either Generalized Crude Oils or Generalized Refined Products; however, thermal expansion factors can be determined and these pure compounds can be treated as a Special Application.

It is recognized that there are some pure components whose densities put them in the range of this Standard and the standard(s) for light hydrocarbons. The two standards give results that are of comparable accuracy but are slightly different. It is up to the contracting parties to decide which is more appropriate to use.



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11 .I .2.5.13 Gasohol

Gasohol is a mixture of gasoline and 10 vol% ethanol. Based on data (available at API) obtained at the University of Missouri - Rolla, gasohol is best represented as a special application with a 60°F thermal expansion factor (a6o) of 714.34~10-~ OF-’.

11.1.3 Outline of Calculation Procedures

In order to produce identical results in 1980 using the computer technology of that day, the 1980 CTL Tables used an integer mathematical method. This method required a set of complex truncation and rounding routines to generate results that would be consistent using different machines. Since the issuance of the 1980 CTL Tables changes in computer hardware, software, and standardization policies have eased this need. The standard computer processor of the early 2000s supports 64-bit floating-point operations. This Standard is designed to use that technology and simplifj the arithmetic associated with the procedure. This Standard reflects the use of floating point mathematical operations where integer creation of decimal numbers is not necessary. However, older computer processor technology, primarily 16-bit chips without math coprocessors (or lower powered technology), may not reproduce the factors exactly to the fifth decimal place, which is the level of precision adopted as a requirement of this revised Standard.

In order to produce exact (to fifth decimal place) factors between two different computers andíor computer software, absolute adherence to the procedure is still required. If the sequence of the procedure is not followed, exact reproduction is unlikely to be achieved. The implementation procedures described herein can, by careful and deliberate application, produce consistent results through the majority of languages and word sizes in present and anticipated future use. Finally, all constants shown must be carried to the exact number of digits as presented and all calculations must be executed using 64-bit calculations as a minimum.

11 .I .3.1 Distinction Between “Standard,” “Base,” “Observed,” and “Alternate” Conditions

The phrases “standard,” “base,” “observed,” and “alternate” conditions are used throughout this Standard.

0 The “observed” condition is the temperature and pressure at which the density of a liquid is actually or assumed to have been measured. Calculations can then be performed to correct this observed density to any other temperature and pressure conditions.

0 The “standard” or “base” condition is a defined combination of temperature and pressure at which liquid volumes are expressed for purposes of custody transfer, stock accounting, etc. The terms standard and base are used interchangeably. Accepted standard temperatures are 60°F, 15°C and 20°C. Accepted standard pressures are zero gauge pressure (for non-volatile liquids at the standard temperature) or the liquid’s vapor pressure at the standard temperature (for volatile liquids).

0 The “alternate” conditions are any other temperature and pressure conditions to which the observed or standard density can be corrected.

The distinction between these conditions may best be shown with an example. Consider a storage tank containing a liquid at an average temperature of 122°F. A sample is withdrawn and the density measured at 85°F. One would like to correct the volume of liquid in the tank to a 60°F standard temperature. In the example, the observed conditions are 85°F and O psig since those are the temperature and pressure at which the density is actually measured. The standard or base condition is 60°F and O psig. However, since the tank is actually at 122°F and O psig, the observed density cannot be directly applied to the tank volume. In this case, the tank’s temperature and pressure of 122°F and O psig are considered as alternate conditions.

The situation is similar for measurements made on flowing liquids. Consider a pipeline with a liquid flowing at 70°F and 150 psig at the flow meter. The density of liquid is measured at 80°F and 145 psig at the densimeter. In this example, the observed conditions are 80°F and 145 psig since those are the temperature and pressure at which the density is actually measured. The standard or base condition is 60°F and O psig. However, since the flowing liquid is actually at 70°F and 150 psig, the observed density cannot be directly applied to the meter volume. In this case, the meter’s temperature and pressure of 70°F and 150 psig are considered the alternate conditions.



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11 .I .3.2 Basic Equations

The correction of the density of a liquid from its base condition to an alternate temperature and pressure condition is given in this Standard as a direct calculation performed in a two part process:

1. A thermal correction is applied to the liquid to account for the change from the base temperature to the alternate temperature along its base pressure.

2. A pressure correction is applied to the liquid to account for the change from the base pressure to the alternate pressure at the alternate temperature.

The temperature correction factor is referred to as the CTL (Correction factor for the effect of Temperature on the Liquid) and can be expressed as CTL . The pressure correction factor is referred to as the CPL (Correction factor for the effect of Pressure on the Liquid) and can be expressed as CpL . The product of these correction factors can be referred to as the CTPL (Correction factor for the effects of Temperature and Pressure on the Liquid) and expressed as CTpL ; this is the full VCF.

Mathematically, the procedure starts with the density p T = p(T, e) (and corresponding volume VT = V(T, e ) ) expressed at the base temperature T and base pressure Pe . Corrections are made to obtain the density p(t, P) (and corresponding volume V ( t , P)) at the alternate temperature t and gauge pressure P. The thermal correction to an intermediate density p(t, Pe) is done first:

and then the pressure correction to p(t, P) :

Note that the combined correction is simply the product of the first two correction factors since:

Volume corrections use the same factors since the volume of a fixed mass is inversely proportional to its density:

The density and volume at temperature t and pressure P can be calculated from the density and volume at base conditions as:



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Densities can be corrected from any observed condition to any other alternate condition by combining the correction factors for each set of conditions. The factors for correcting the observed density po = p(to,Po) to the standard conditions are defined as:

then the correction from p(to , Po) to p( t , P ) can be calculated from:

The correction for the volume is:

11.1.3.3 Calculation of CTL and CPL Factors in This Standard

The specific equation forms for the temperature and pressure correction factors used in this Standard are:

C, = exp( -a, ( t - T ) [i + 0.8a, ( t -T + 6,)]}

= exp (-a,At [ 1 + 0.8a, (At + 6,)])

1 C P L = 1 - Fp(P - P,) '

where aT is the thermal expansion coefficient at the base temperature T , At is the difference between the alternate temperature and the base temperature, Fp is the compressibility coefficient, and 6, is a small base temperature correction value.

In the 1980 Standard, aT was correlated to the density at a 60°F base temperature and O psig pressure, p* , and is denoted as a60. The CTL equation was developed as a correction to 60°F density, so T = 60 and 6, = O . Fp was correlated to this same base density and the temperature t at which the compression occurs. The forms for these correlations are:

K o + K l p * + K 2 p y KO KI am = =?+*+K2 P*2 P P



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There was one set of coefficients for the Fp compressibility factor (the A , B , C , and D values) but several sets of coefficients for the a, thermal expansion coefficient (the KO , Ki , and K2 values) depending upon the liquid’s classification and density at 60’F.

To recognize differences between the current ITS-90 temperature scale and the IPTS-68 temperature scale in effect when the data for this Standard were measured, this Standard makes small corrections to the temperature t and the base temperature T and a non-zero base temperature correction factor, denoted as 6,, , is used. Also, the density used in the correlations, p* , is slightly different from a p, measured consistent with ITS-90. See 1 1.1.5.3 for the procedure to convert ITS-90 temperatures to an IPTS-68 basis, Appendix C for the origin of the 6, correction factor, and 1 1.1.6.1 for the calculation of p* from p, .

Equations (16) and (17) are directly expressed in terms of p* . However, since p* can be directly related to p,,,

then these equations can also be thought of as being a direct function of p, , too.

11 .I .3.4 Base Pressure in This Standard

For volatile hydrocarbons, the base pressure is the saturation pressure for the liquid (i.e., its “bubble point” pressure). It is generally assumed that if the saturation pressure is less than atmospheric pressure then there is little error in applying the correction at a constant base pressure of 1 atmosphere. The heavier liquids covered by this Standard are fairly non-volatile - the saturation pressure is less than the atmospheric pressure over the entire temperature range of this Standard. It is only the lightest of the liquids covered by this Standard whose vapor pressures may exceed atmospheric pressure at the higher temperatures.

For simplicity of application, this Standard will neglect any effects of the liquid’s saturation pressure exceeding atmospheric pressure. In all equations, this Standard will use P, = O (gauge) and the CPL equation reduces to:

1 1-FpP‘

CPL =-

11 .I .3.5 Iteration Scheme to Determine Base Density from Observed Density

Because a60 and Fp in Equations (16) and (17) are direct functions of the 60’F density p60, the CTL and CPL equations are also direct functions of &o. When a given is used to calculate a corresponding density p , then these equations are very convenient to use. However, if an observed density p, is given and the corresponding p60 is to be calculated, then these equations are not so convenient. Equations (16) and (17) cannot be rearranged so that

can only be determined numerically using a process of “iteration.” Iteration is a process by which p60 is repeatedly guessed until the p calculated at the observed conditions matches the observed density p, .

can be directly calculated from p, . In this case, the

The following six steps are a general iterative procedure to calculate p60 from a given p, :

1. Start the procedure by estimating a value for p60.

2. Start an iterative step. Calculate the p value at the observed conditions using the current estimate of p60

o Determine the value of p; consistent with the current estimate of p, .

0 Calculate the a 6 0 value using Equation (16) (unless the calculation is for a Special Applications liquid and the a60 is a given, constant value). Calculate the CTL using Equation (14).

0 Calculate the Fp value using Equation (1 7). Calculate the CPL using Equation (1 8).



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0 Calculate the p value at the observed conditions using Equation (7).

3. Compare the given observed density p, to the calculated density at observed conditions p.

4. If the difference between the given observed density p, and the calculated density at observed conditions p is acceptably small, then no further iterations need be done. Terminate the iterative process by going to Step 6.

If the difference is not acceptably small, then estimate a new process by returning to Step 2. This finishes an iterative step.

The final p60 value is the desired output from this iterative procedure. This finishes the iterative procedure.

5. value and continue the iterative

6.

The iterative process as described will continue until the convergence criterion of Step 4 is achieved. Sometimes it is practical to establish an upper limit on the number of iterations allowed. When this is added, an additional check is added at the start of Step 2 to stop the calculations if the maximum number of iterations has been exceeded. If so, the iterations are stopped even though convergence has not been achieved. A special error condition is returned to signify non-convergence. The actual form of this error condition is not specified by this standard.

The nature of the iterative process is most significantly defined by how the new value for p60 is determined in Step 5. The 1980 CTL Tables were created using a “Direct Substitution” method - it was a simple iterative procedure to explain, but was neither powerful nor robust. The Direct Substitution method was prone to converge very slowly (or not at all) for some observed density values, especially those near the boundaries of the sub-groups for the Refined Products. For this revision, there was a need for a powerful iteration procedure; this need was made even greater by the inclusion of the pressure correction term in the procedure. For this reason, a more sophisticated “Newton’s Method” is used.

Newton’s method defines a specific way to calculate a new p60 value from the previous value in Step 5 above. The non-linear Equations (16) and (17) are “linearized” about each estimate of the value. The equations are linearized by taking the derivative of all of these equations with respect to p60. This linearized equation can then be directly solved for a value of that gives the observed density p, . The solution of the linearized equation is used as the next iterative step’s estimate for p60.

Newton’s methods have two important properties: (1) when an estimate is near the actual answer, the method is guaranteed to converge and (2) the convergence of the estimate to the correct answer is very quick. These properties give the power and robustness needed in this Standard.

The derivation of the iteration equations is in Appendix F. The detailed steps to implement the iterative procedure (e.g., how to make the initial estimate, checks to keep values in bounds, convergence tolerances, etc.) are in 11.1.6.2.

11.1.3.6 Calculation of CTL and CPL Factors for Base Temperatures Other Than 60°F

The goal of this Standard is to provide consistent results when performing corrections using either metric or customary units. That is, when one corrects an observed density to the density at alternate conditions of temperature and pressure, the same result should be obtained irrespective of the base conditions used or the units in which they are expressed. For the equations and correlations used in this Standard, the 60°F base condition must always be applied in the calculation procedure, even when input and output data are expressed in the metric system of units.

It was a desire in this revision to modify the equations in 1 1.1.3.3 to enable direct input of densities at each separate base temperature (60°F, 15OC and 2OOC). Unfortunately this proved impossible to achieve while keeping all calculations consistent. Because of this, the 60°F base condition must be incorporated into all of the CTL and CPL calculations used in this Standard. See Appendix C for details.



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11 .I .3.7 Calculation Types

Based upon the equations used for this Standard, there are three distinct types of calculations when using the 60°F base density. These particular classifications are based upon how the calculations are performed - each calculation type requires the preceding type(s):

Type 1. Starting with the density at the 60°F and O psig base condition, correct the density (and volume) to an alternate temperature and pressure condition.

Type 2. Starting with an observed density at its temperature and pressure, correct the density (and volume) back to the 60°F and O psig base condition.

Type 3. Starting with an observed density at its temperature and pressure, correct the density (and volume) to an alternate temperature and pressure condition.

A Type 1 calculation is straightforward - starting with the density at 60°F and O psig all parameters can be determined and the calculations can proceed in a “feed-forward” manner. No iterations are involved in this type of calculation. A Type 2 calculation is more complicated - this requires a set of Type 1 calculations, iterating upon the value of the 60°F and O psig density. A Type 3 calculation is a combination of a Type 2 calculation followed by another Type 1 calculation.

All calculations involving metric base temperatures are Tvpe 3 calculations. The corresponding metric calculation types are:

Type 1M. Starting with the density at the metric base condition, correct the density (and volume) to the alternate temperature and pressure condition. This is a Type 3 calculation - the density at the metric base condition is the “observed density” and the correction is made to the alternate temperature and pressure condition after first calculating the value of density at 60°F and O psig.

Type 2M. Starting with an observed density at its temperature and pressure, correct the density (volume) to the metric base condition. This is also a Type 3 calculation - the alternate temperature and pressure condition is now the metric base condition.

Type 3M. Starting with an observed density at its temperature and pressure, correct the density (volume) to the alternate temperature and pressure condition. This description is identical to the non-metric Type 3 calculation description. If the density at the metric base condition is required, however, then an extra Type 1 calculation must be performed.

The pipeline example given previously is an example of a Type 3 calculation. The density at the observed conditions at the densimeter is first corrected to the standard condition of 60°F and O psig. The final step is to adjust this standard density to the alternate conditions at the flow meter.

11 .I .3.8

The correlations for the 60°F thermal expansion factor give results for an “average” liquid of a specific commodity type. However, there may be occasions when one wants to make density measurements on a particular liquid in order to determine its actual a60 value. An implementation procedure is presented in 1 1.1.5.2 to derive &o and a60 values from a set of density measurements. The following are general guidelines that should be followed before the data analysis is done:

Calculating the Thermal Expansion Factor for Special Applications

0

0

A minimum of 10 data points is needed to use this method.

The data measurements should cover the temperature range over which the VCF values are to be used. The range should include 60°F even if a measurement is not made at this temperature.

0 The density measurements should be made at such pressures that a pressure correction need not be applied (i.e., the CPL factor is 1 for all of the data points).



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11 .I .3.9

Previous versions of the Table values required rounding at various stages of the calculation procedures. The Implementation Procedures are now written with no rounding of initial or intermediate values. The final VCF is rounded to five decimal places. Rounding of input values is only to be used when creating tabular representations of the results from these Implementation Procedures. When the tabular representations are calculated, the initial and final values are to be rounded for display, but intermediate values are never to be rounded.

11.1.3.10 Glass Hydrometer Corrections

Rounding of Values

When a glass hydrometer is used to measure the density of a liquid, special corrections must be made to account for the thermal expansion of the glass when the temperature is different from that at which the hydrometer was calibrated. The 1980 CTL Tables had generalized equations to correct glass hydrometer readings and made these corrections part of the printed odd-numbered Tables. However, the detailed procedures to correct a glass hydrometer reading are beyond the scope of this Standard. The user should refer to the appropriate sections of API MPMS Chapter 9 or other appropriate densityíhydrometer standards for guidance.

11.1.3.1 1

The International Committee for Weights and Measures, CIPM, publishes the international temperature scale. Its purpose is to define procedures by which specified practical thermometers of the required quality can be calibrated in such a way that the values of temperature obtained from them can be precise and reproducible while at the same time closely approximating the corresponding thermodynamic values. The temperature scale provides defined values of temperature for various phenomena (e.g., the triple point of water is defined to be 273.16 K and the freezing point of tin is 505.078 K) and a means to interpolate temperature values in between the fixed points.

See Appendix D for a detailed description of the International Temperature Scale.

Since the international temperature scale is used for the calibration of thermometers, the values of temperature- dependent physical parameters of materials will, in principle, depend on what scale is in force at the time the parameter is measured or referenced. However, since changes between scales are relatively small, this effect will only become noticeable at high levels of precision.

International Temperature Scale of 1990, ITS-90

The data collected for the 1980 version of the CTL Standard and used to develop the correlations were based on measurements made with the IPTS-68 temperature scale, in force from 1968 to 1990. However, current temperature measurement devices are calibrated consistent with the ITS-90 temperature scale that superseded IPTS-68 in 1990. -

A subtle effect of the change of temperature scale is that the customary standard temperature, 60°F, has undergone a slight shift. What is 60°F in ITS-90 is an equivalent 60.007"F in IPTS-68. Because of this, any input pm values

determined today must be corrected to an equivalent IPTS-68 60°F value, p* , before the value can be used in the am and F, correlations, Equations (1 6) and (1 7), respectively.

11 .I .4 Summary and Precision Statement

The changes made to this Standard are primarily oriented to the computer application of the underlying equations. The underlying equations have not been substantially changed. Therefore, that the Precision Statement made for the 1980 CTL Tables and 1981 Compressibility Tables are still valid for this version.

The 1980 CTL Tables were based on density temperature determinations made by the U.S. National Bureau of Standards from 1974 to 1979 under contract to the API on 225 samples of products ranging from heavy fuel oil to gasoline blend components and 124 samples of crude oil that covered a wide range of quality and represented about 45% of the world's crude production and reserves as known during that time period. The thermal expansion properties (volume correction factors) for products (including lube stocks) and crude oils were correlated in separate, generalized tables as a function of temperature and density or API gravity. The predicted precision at the 95% confidence level was:



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CTL precision at 95 % confidence level

Temperature 100°F 150°F 200°F 250°F

Crudes and Products +0.05% +O. 15% +0.25% +0.35%

A precision statement for the 250°F to 300°F portion of the tables has not been given because it is an extrapolation.

For the 1981 Compressibility Tables, the maximum compressibility factor uncertainty was estimated to be +6.5% at the 95% confidence level. Hence at worst, one should expect that the real compressibility factor for a given material could be either 6.5% higher or 6.5% lower than the value in the Standard. This statement is only true within the limits of the database. It may not be true for the extrapolated portions of the Standard. To assess the possible uncertainty in the calculated volume at equilibrium pressure using the above database and equation, two approaches were taken. First it was assumed that only the correlation uncertainty in mean compressibility of +6.5% was significant. With this approach, volumetric uncertainties due to pressure effects should be in the range of 0.02 to O. 1 O%, depending on operating conditions.

11 .I .5 Implementation Procedures - General

The methods needed to calculate the Volume Correction Factors follow in 1 1.1.5, 1 1.1.6, and 1 1.1.7. These methods are called Implementation Procedures.

Auxiliary calculations are presented first in 11.1.5:

0 Converting the units of input values to those used by the calculation routines.

0 Calculating the thermal expansion factor from measured density data.

0 Calculating the equivalent IPTS-68 temperature value given an ITS-90 temperature value.

0 Rounding the values used in this Standard.

The core calculation methods using the 60°F base temperature are presented in 1 1.1.6:

0 Starting with the density at the 60°F base condition, correct the density (and volume) to the alternate temperature and pressure condition. (Type 1 calculation)

0 Starting with an observed density at its temperature and pressure, correct the density (and volume) back to the 60°F base condition. (Type 2 calculation)

0 Starting with an observed density at its temperature and pressure, correct the density (and volume) to some alternate temperature and pressure condition. (Type 3 calculation)

Calculation methods for temperature bases other than 60°F are presented in 1 1.1.7. They make use of the non- metric calculation routines.

All calculations shall be performed using at least double precision (i.e., long floating point, eight byte, or 64-bit) arithmetic. This should allow the computer program to recognize the difference between 1 .O and 1.0 + E for absolute values of E on the order of are used for all calculations.

or smaller. This also means that approximately 16 or more decimal digits

The procedures require no rounding of initial, intermediate, and most final values. The only value to be rounded is the combined temperature and pressure volume correction factor, CTPL. However, for practical reasons of presentation, rounding is used when creating tabular representations of the results from these Implementation Procedures.

Examples of the calculations are presented at the end of the sections with the Implementation Procedures. Even though double precision was used for these example calculations only twelve decimal digits are printed here. If



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these examples are used to test one's own computer implementation of the procedures, it is required that at least eight of the significant digits be matched.

11.1.5.1 Density-Related Values

Method to Convert Units of Temperature, Pressure, Thermal Expansion Factor, and

Outline of Calculations

This procedure accepts the density, temperature, and pressure values in units as entered and converts them to the units required by the calculation procedure.

Relative density & AF'I gravity values are in vacuo.

Possible Input and Output Values

LC

''a

'bar

Y T

Y 60

G

a60,"C

P

t

P

a60

Temperature value (OC)

Pressure value ( H a (gauge))

Pressure value (bar (gauge))

Relative density value based upon water at temperature T

Relative density value based upon water at 60°F

AF'I gravity (OAF'I)

60°F thermal expansion factor (OC-')

Density value (kg/m3)

Temperature value (OF)

Pressure value (psig)

60°F thermal expansion factor (OF-')

Calculation Procedure

Step 1 : Convert the units of the input variables to those required by the procedure: kg/m3 for density, OF for temperature, psig for pressure, and OF-' for the 60°F thermal expansion factor.

Temoerature

If the input temperature variable is in OF units then no processing is required.

If the input temperature variable is in "C units then:

t = 1.8-toc +32

Pressure

If the input pressure variable is in units of psig then no processing is required.

If the input pressure variable is in units of kPa then:



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P = 'pa

6.894757 .

If the input pressure variable is in units of bar then:

P = 'bar

0.06894757 .

Densitv

If the input density variable is relative density then:

where pw,T is the density of water consistent with the reference temperature T . The only water density needed in this Standard is for 60°F. The accepted value for the density of water at 60°F is 999.016 kg/m3 (see Appendix D).

If the input density variable is M I gravity then:

999.016 p=- 141.5 - 141.5 G+131.5 pw,60 -

If the input density variable is already in units of kg/m3 then no processing is required. However, there are instances in this Standard that the density in units of kg/m3 must be converted back to M I gravity or relative density. If the 60°F relative density is required, then:

P - P Y60 = pW.60 - 999.016

or if the M I gravity is required, then:

131.5 = 141.5 - 131.5 G - 141.5 P/Pw,So p/999.016

60°F Thermal ExDansion Factor

If the input 60°F thermal expansion factor variable is in units of OF-' and the output is also OF-' then no processing is required.

If the input 60°F thermal expansion factor variable is in units of O C - ' and the output is also O C - ' then no processing is required.

If the input 60°F thermal expansion factor variable is in units of O C - ' and the output is OF-' then:

a60,"C = -. 1.8

If the input 60°F thermal expansion factor variable is in units of OF-' and the output is O C - ' then:

Step 2: Exit from this procedure.



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11 .I S.2


Method to Calculate Thermal Expansion Factor from Density Measurements

This procedure accepts measured density values and derives values of the density at 60°F (p60) and the thermal expansion factor at 60°F (a6o). The following are general guidelines for the data analysis:

0 A minimum of 10 data points is needed to use this method.

0 The data measurements should cover the temperature range over which the VCF values are to be used. The range should span 60°F even if a measurement is not made at this temperature.

0 The density measurements should be made at such pressures that a pressure correction need not be applied (i.e., the CPL factor is 1 for all of the data points).

This procedure results in a a 6 0 value in units of OF-'. However, if units of OC-' are required then use the procedure in 1 1.1.5.1 to convert as appropriate.

Input Values

fl

t i

Number of measured density values

Individual temperature value for which there is a density measurement (OF)

Pm, i Individual density measurement (kg/m3)

Output Values

a60 Thermal expansion factor at 60°F (OF-')

P60 Density at 60°F (kg/m3)

Intermediate Values

Temperature shift value (a constant, 0.0 1374979547OF)

Shifted individual temperature values (OF)

Difference between an individual temperature value and the base temperature (OF).

Summations of the Ati and pm,i values needed to perform the regression. There are eight different summations needed; each will be identified by their subscript ( j ) .

Coefficients for the cubic equation that will define the thermal expansion coefficient. There are 4 different coefficients; each will be identified by their subscript ( j ) .

Value of the thermal expansion factor on the m-th iteration (OF-')

Change added to the value of a ( m ) on the m-th iteration to get the value for the next (m+l)-th iteration (OP')


Step 1 : Shift the input temperatures ti to t; following the procedure in 1 1.1.5.3.

Step 2: Calculate the differences of the individual temperatures from the base temperature:



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Ati = ti* - 60.00687490.

Step 3: Calculate the summations of the Ati and pm,i values needed to perform the regression. These are:

i=l

N S, = c A t i

i=l

N SIP = Ati . lnpm,i

i=l

N S, = c ( A t i ) ’

i=l

N S, = c ( A t i ) 3

N S , = c ( A t i ) 4

i=l

Step 4: Calculate the coefficients for the cubic equation that will define the thermal expansion coefficient:

spst a, =Sip -- N

S: +1.6(Sn +6,Sf)Sp

N a, =Sn+1.6(Snp+6,Sfp)-

N

N S, +(2S, +6,Sn)6, -

Step 5: Initialize the estimate for the thermal expansion factor, a(1):

Initialize iteration counter as m = 1 and start iterations.

Step 6: Determine a correction to the current iterative value of a(m) :



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Step 7: Update the value for a ( m + 1 ) :

a ( m + ' ) = a ( m ) + Aa(m)

Step 8: Go to Step 4 and repeat iteration five times.

Step 9: After the 6* iteration, set the values of a6, and p6, :

a 6 0 =a(6)

S, + [ S f +0 .8(S , +G,S,)a,]a, N P60 = exP

Step 10: Round the values of a6, and P60 to be consistent with 11.1.5.4.

Step 1 1 : Exit from this procedure.

Example

The following table shows experimental data for a specific petroleum fluid. From these data the a 6 0 and &o values are desired.

"C kg/m3

14.9 868.21

15.9 867.50

20.2 864.5 1

25.0 861.19

29.6 857.91

32.9 855.62

35.4 853.82

40.2 850.48

42.0 849.16

44.9 847.15

The following tables show: the original data; the data manipulated to be put into the proper units; intermediate summations and equation coefficients; the iterative results; and the final a6, and p6, values.



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Original Data

ti Pm,i

Manipulated Data

ti ti* Ati lnPm,i

I OC I kg/m3 I OF I OF I OF I I

15.9

20.2

I 14.9 I 868.21 I 58.82 I 58.8266 I -1.1803 I 6.76643 I 867.50 60.62 60.6270 0.6202 6.76562

864.5 1 68.36 68.3690 8.3621 6.762 16

29.6

32.9

I 25.0 I 861.19 I 77.00 I 77.0113 I 17.0044 I 6.75832 I 857.91 85.28 85.2934 25.2866 6.75450

855.62 9 1.22 91.2350 3 1.228 1 6.75 183

40.2

42.0

I 35.4 I 853.82 I 95.72 I 95.7362 I 35.7293 I 6.74972 I 850.48 104.36 104.3785 44.37 16 6.74580

849.16 107.60 107.6 194 47.6125 6.74425 I 44.9 I 847.15 I 112.82 I 112.8408 I 52.8339 I 6.74188 I

I Summations I Coefficients in Equation for a60

I N I 10 I a0 I -1.55568

I 3296.87

I Spp =z(lnpm,i)2 I 456.173 a2 I 411,305

I S, = E M i I 261.868 a3

I S, =c(At i ) ’ I 10279.26

I S, = c ( A t i ) 3 I 440511

I ,”, = c ( A t i ) 4 I 19885457.5

I 1 I 4.54646E-O4 I -7.98343E-O6 I I 2 I 4.46663E-O4 I -7.42106E-09 I I 3 I 4.46655E-O4 I -6.40949E-15 I I 4 I 4.46655E-O4 I O.OOOE+OO I I 5 I 4.46655E-O4 I O.OOOE+OO I I 6 I 4.46655E-O4 I O.OOOE+OO I

The resulting coefficient of thermal expansion (to six digits) is am = 446.655~ at 60°F (to six digits) is p60 = 867.756 kg / m?. When rounded consistent with 1 1.1.5.4 the results are am = 446.7 x

OF-’ and the calculated density

OF-’ and pm = 867.8 kg/m3 .



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11 .I 5 3


Method to Convert Temperature from ITS80 to IPTS-68 Basis

This procedure converts temperature from ITS-90 to IPTS-68 basis. This correction is necessary because of the change in the standard procedure to calibrate temperature measurement devices. The change in the temperatures between the two scales is small. The equation presented here is from the original paper describing the ITS-90 temperature scale.2

Input Values

tF,90 Temperature consistent with ITS-90 (OF)

tc,go Temperature consistent with ITS-90 (“C)

Output Values

tF,68 Temperature consistent with IPTS-68 (OF)

tc,68 Temperature consistent with IPTS-68 (“C)

Intermediate Values

At Correction to ITS-90 temperature to give IPTS-68 temperature (“C)

7 Scaled temperature value.


Stepl: Accept input temperature value, either in units of O F , tF,90 , or OC, tc,go .

Step 2: If input temperature was in units of O F , calculate the temperature in units of OC:

tF,90 -32 tc,w = ~ 1.8

Step 3. Calculate the scaled temperature value:

and use this to calculate the temperature correction:

The ai coefficients are given in the following table.

2 “The International Temperature Scale of 1990, ITS-90,” NPL Special Report QU S45, National Physical Laboratory, Teddington, Middlesex, November 1989.



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i -0.148759 -0.267408 1 .O80760 1.269056

-4.089591 6 -1.871251 7 I 7.438081 8 I -3.536296

Step 4. Determine the equivalent IPTS-68 temperature:

If the input temperature was in units of OF, also calculate the equivalent IPTS-68 temperature in customary units:

tF,68 = 1 .8tc,68 + 32


11 .I S.4


Rounding of Values

This procedure gives instructions and increments for rounding density, temperature, pressure, thermal expansion coefficient, and volume correction factor values. These rounding rules are needed to generate the final volume correction factor due to temperature and pressure and to generate the tables in printed tabular (historical) format. All input values must be rounded when generating the tables in historical format.


Step 1: The following table shows acceptable units for the input and calculated variables and the increment to which they should be rounded.

I Variable Type Units Rounding Increment (6) Density OAPI

Relative Density

kg/m3

o. 1

0.0001

o. 1

Temperature OF

OC

o. 1

0.05

Pressure 1

5

0.05

Thermal Expansion Coefficient ( ( 3 6 0 ) OF-'

oc-'

0.0000001 (o.1x10-6)

(0.2x10-7 0.0000002

CTL 0.00001

Scaled Compressibility Factor ( F p ) psi-' 0.001



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Wa-'

bar-'

0.0001

0.01

I CPL 0.00001 I I CTFJL 0.00001 I

Step 2: Normalize the input variable.

where X is the value to be rounded, 1x1 is its absolute value, 6 is the rounding increment, and Y is the normalized variable.

Step 3: Find the integer closest to the normalized variable. If the decimal portion of Y is not exactly equal to 0.5 then use the following equation for rounding:

I =trunc(Y+0.5)

where trunc is the truncation function and I is the rounded value for the normalized variable. However, if the decimal portion of Y is exactly equal to 0.5 then use the following equation for rounding:

if trunc(Y) is odd if trunc( Y) is even .

Step 4: Rescale the integer from Step 3:

Xrmn, = + 6 - I

where Xround is the rounded variable. The sign of the rounded value is chosen to match that of the original value.


Examples

A temperature of 5.34"C is rounded as:

y = L - 5.341 -106.8

0.05

I =trun~(106.8+0.5)=trun~(107.3)=107

Xrm,,, = +0.05-107 = +5.35

A temperature of -5.34"C is rounded as:

5.341 Y =k =106.8

0.05

I =trun~(106.8+0.5)=trun~(107.3)=107

Xrm,,, = -0.05-107 = -5.35



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A temperature of 10.05'F should be rounded as follows:

y = l - 10.051 -100.5 o. 1

I = trunc (1 00.5) = 1 O0 (rounding towards the even integer)

xrmn, = +o. 1.100 = 10.0

11 .I S.5 Other Implementation Considerations

0

0

0

CTPL should be substituted for CTL x CPL, where a standard specifies a serial multiplication of correction factors. Where a calculation within an existing standard makes use of a CTL factor alone, an equivalent value CTPL is calculated with observed gage pressure set to zero. In this document, the final VCF (CTPL) is rounded to five decimal places. Different rounding precisions may be used to accommodate other standards, however they should not exceed eight decimal places.

11.1.6 Implementation Procedures for Customary Units (60°F and O psig Base Conditions)

11.1.6.1 Method to Correct a Measured Volume to Base Conditions and Density from Base Conditions to an Alternate Temperature and Pressure


This procedure calculates the Volume Correction Factor (VCF) for correcting from the density at the base conditions (60'F and O psig) to alternate temperature and pressure conditions. The parameters used in this procedure depend upon the commodity group to which the liquid belongs. This calculation is done as a two-part process:

1. A thermal correction is applied to the liquid to account for the change from the base temperature (60'F) to the alternate temperature at a constant base pressure.

2. A pressure correction is applied to the liquid to account for the change from the base pressure (O psig) to the alternate pressure at the alternate temperature.

The procedure has the flexibility of accepting a pre-calculated 60'F thermal expansion factor or calculating one based upon the commodity type of the liquid.

The calculation routine is depicted in Figure 1 1.1.6.1 .A.

The procedure has been written assuming that the input values are all in the proper units (OF, psig, and kg/m3). If they are not in the proper units then apply the procedures in 11.1.5.1 before entering this procedure. The density values calculated by this procedure are in the units of kg/m3. If these units do not match the original input units, then the output densities should be converted to that of the original input value's units using the procedures in 11.1.5.1.

Input Values

Commodity group describing liquid (if a 6 0 not input)

a60 Pre-calculated 60'F thermal expansion factor (if commodity group not given) (OF-')

P 60 Density at base conditions (60'F and O psig) (kg/m3)

t Alternate temperature (OF)



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P Alternate pressure (psig)

Optional Input Values

Volume at alternate conditions (t and P) (any valid set of units, such as barrels, liters, and cubic metres)

Output Values

CTL

CpL

Fp Scaled compressibility factor (psi-')

CTpL

Optional Output Values

P

V,,

Intermediate Values

Volume correction factor due to temperature

Volume correction factor due to pressure

Combined volume correction factor due to temperature and pressure

Density at alternate conditions (kg/m3)

Volume at base conditions (60'F and O psig) (same units as V,,)

Temperature shift value (a constant, 0.0 1374979547'F)

Alternate temperature shifted to IPTS-68 basis (OF)

Base density shifted to IPTS-68 60'F basis (kg/m3)

Alternate temperature minus the base temperature of 60'F (OF)

Thermal expansion factor at 60'F (OF-') (if not input)

Coefficient in correlation for a 6 0 (kg2/m6 OF)

Coefficient in correlation for a 6 0 (kg/m3 OF)

Coefficient in correlation for a 6 0 (OF-')

A , B Variables used in calculation of p* .


Stepl: Unless otherwise directed, check the input values to determine if they are in the range of this Standard. The following are the valid limits.

-58.0'F < t < 302.0'F

O < P < 1500 psig

p60,min < p60 < póO,- (if commodity type is specified)

230.0 x 10-6 OF-' < a60 < 930.0 x 10-6 OF-' (if a60 , not commodity type, is specified)



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The following table gives the p60 limits for the various commodity groups. This check does not have to be done if a60 , not the commodity group, is specified.

I Commodity Type I P60,min I P60,max

6 10.6 kg/m3

Lubricating Oil 800.9 kg/m3

1163.5 kg/m3

If P < O psig then set P = O psig and continue with the procedure.

If any of the other conditions are not true then one or more of the input variables is out of range. Set an error condition (such as setting all output values to zero) and exit procedure.

Step 2: Shift the input temperature t to the IPTS-68 basis t* following the procedure in 1 1.1.5.3.

Step 3: Shift the input p60 value to the IPTS-68 basis p* . If apre-calculated a60 value has been input, use:

If the commodity group has been specified, then compute the p* value using:

exp [ A( 1 + 0.8A)I - 1 1+ A(l+l.óA)B

where:

The Ki coefficients used in these equations depend upon the commodity group. The following table gives the coefficients to be used.

Density Range(kg/m3)

Step 4: In preparation of calculating the correction factor due to temperature, C,, , determine the coefficient of thermal expansion at the base temperature of 60°F, a 6 0 . If a pre-calculated a 6 0 value has been input, proceed to Step 5.



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SECTION 1 - VOLUME CORRECTION FACTORS FOR CRUDE OILS, REFINED PRODUCTS, & LUBE OILS

If the commodity group has been specified, then compute the a60 value using:

33

Step 5:

Step 6:

Step 7:

Step 8:

Step 9:

The coefficients used in this equation depend upon the commodity group. Use the same coefficients that were used in Step 3.

Calculate the difference between the alternate temperature and the base temperature as:

At = t* - 60.0068749.

Use this value to calculate the correction factor due to temperature, C T L :

C, = exp ( -a,At [ 1 + 0.8a, (At + õ,)]) where 6, = 0.01374979547 .

Calculate the scaled compressibility factor Fp . Use the equation:

793920+ 2326.0-t* -1.9947+0.00013427-t* +

P*2

Calculate the correction factor due to pressure, CpL . Use the equation:

1 ~ - ~ o - ~ . F , . P . C P L =

Calculate the VCF, the combined temperature and pressure correction, C T p L :

CTPL = CTL . CPL .

Round this value of CTpL consistent with 1 1.1.5.4.

Optionally, correct a volume measured at alternate condtions to base conditions and/or correct base density to alternate conditions.:




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34 SECTION 1 - VOLUME CORRECTION FACTORS FOR CRUDE OILS, REFINED PRODUCTS, & LUBE OILS

Figure 11.1.6.1.A Flow Chart Of Procedure Correcting Volume and Density to an Alternate Temperature and Pressure from Base Conditions

Enter pa, t, P, &

Yes T

Determine t* and p* values

Determine KO, KI, & &. Compute a60

Compute C,

Set CpL=i

I Yes T

Compute Fp & CpL

Compute C, = C,CpL

'= '60"TPL



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Example Calculations A P I MPMS 11.1.6.1 Customary Units, Example 1

A volume o f a crude o i l i s measured a t observed condit ions o f temperature and pressure. The base A P I i s known. ca lcu la te the volume a t base condit ions and cor rec t the base density t o an a l te rna te condi t ion.

Commodity ...................... Generalized crude O i l t a l te rna te temperature, 'F .... -27.7 P a l te rna te pressure, PSI ...... O Base API g rav i t y ............... 17.785 volume a t a l te rna te t & P ...... 987.99

Input Data

computed Data - l a s t d i g i t i s rounded f o r display purposes

Calculat ion o f Intermediate Results

step 1 - check input values f o r range excursion

Density kg/cu mete r (Rho60) .... 946.918739324112

A l l i npu t values w i th in range

Calculat ion o f volume cor rec t ion fac to r

step 2 - S h i f t temperature t t o IPTS-68 temperature scale t corrected t o IPTS-68 (t*) .... -27.712499233089

step 3 - S h i f t Rho60 t o IPTS-68 temperature scale KO ............................. 341.095700000000 K I ............................. 0.000000000000 K2 ............................. 0.000000000000 A .............................. 0.000002615273 B .............................. 2.000000000000 Rho60* ......................... 946.921215770785

Step 4 - Determine coe f f i c i en t o f thermal expansion nlpha60 ........................ 0.000380407044

step 5 - ca lcu la te temperature cor rec t ion fac to r C t l de l ta t ........................ -87.719374133089 C t l ............................ 1.033011591958

FP f o r ps i ..................... 0.305779891997

cp1 ............................ 1.000000000000

step 6 - ca lcu la te scaled compressibi l i ty f ac to r Fp

step 7 - ca lcu la te pressure cor rec t ion fac to r cp l

step 8 - ca lcu la te the volume Correction Factor Ctpl Ctpl ........................... 1.033011591958 Ctpl , rounded .................. 1.03301

step 9 - ca lcu la te volume a t base condit ions and density a t a l ternate condit ions

volume a t base condit ions ...... 1020.6035499 oensity a t t & P, kg/cu m ...... 978.1780343640

A P I a t t & P .................. 13.0143512059



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A P I MPMS 11.1.6.1 Customary Units, Example 2 A volume o f a crude o i l i s measured a t observed condit ions o f temperature and pressure. The base A P I i s known. ca lcu la te the volume a t base condit ions and cor rec t the base density t o an a l te rna te condi t ion.

Commodity ...................... Generalized crude O i l t a l te rna te temperature, 'F .... 301.93 P a l te rna te pressure, PSI ...... 1500 Base API g rav i t y ............... - 10 volume a t a l te rna te t & P ...... 285.5

Input Data







step 2 - S h i f t temperature t t o IPTS-68 temperature scale t corrected t o IPTS-68 (t*) .... 301.993163042978

step 3 - S h i f t Rho60 t o IPTS-68 temperature scale KO ............................. 341.095700000000 K I ............................. 0.000000000000 K2 ............................. 0.000000000000 A .............................. 0.000001732357 B .............................. 2.000000000000 Rho60* ......................... 1.16346509372e+03


step 5 - ca lcu la te temperature cor rec t ion fac to r C t l de l ta t ........................ 241.986288142978 C t l ............................ 0.938051116886

step 6 - ca lcu la te scaled compressibi l i ty f ac to r Fp FP f o r ps i ..................... 0.427958509999

step 7 - ca lcu la te pressure cor rec t ion fac to r cp l cp l ............................ 1.006460852301




A P I a t t & P .................. -2.8076041994



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A P I MPMS 11.1.6.1 Customary Units, Example 3 A volume o f a re f ined product i s measured a t observed condit ions o f temperature and pressure. The base API i s known. ca lcu la te the volume a t base condit ions and cor rec t the base density t o an a l te rna te condi t i on.

Commodi t y ...................... General i zed Refined product t a l te rna te temperature, 'F .... 48.04 P a l te rna te pressure, PSI ...... -7.3

Base API g rav i t y ............... 19.4 volume a t a l te rna te t & P ...... 12002

Input Data

Forcing negative pressure t o zero








step 3 - S h i f t Rho60 t o IPTS-68 temperature scale

KO ............................. 103.872000000000 K i ............................. 0.270100000000 K2 ............................. 0.000000000000 A .............................. 0.000002795957 B .............................. 1.291041575770 Rho60* ......................... 936.787006219757


using fue l o i l coe f f i c i en ts :

step 5 - ca lcu la te temperature cor rec t ion fac to r C t l de l ta t ........................ -11.962996740394 C t l ............................ 1.004858068990

step 6 - ca lcu la te scaled compressibi l i ty f ac to r Fp

step 7 - ca lcu la te pressure cor rec t ion fac to r cp l

FP f o r ps i ..................... 0.384339609206

cp1 ............................ 1.000000000000

S t e D 8 - ca lcu la te the volume Correction Factor Ctpl .. 1.004858068990 ctp1 ..........................

c t p l , rounded ............... step 9 - ca lcu la te volume

and density a t a volume a t base condit ions ... oensity a t t & P, kg/cu m ...

A P I a t t & P ...............

. . 1.00486

a t base condit ions ternate condit ions .. 12060.32972 .. 941.3353501926 .. 18.6704615375



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A P I MPMS 11.1.6.1 Customary Units, Example 4 A volume o f a re f ined product i s measured a t observed condit ions o f temperature and pressure. The base r e l a t i v e density i s known. ca lcu la te the volume a t base condit ions and correct the base density t o an a l te rna te condi t ion.

Commodi t y ...................... General i zed Refined product t a l te rna te temperature, 'F .... 85 P a l te rna te pressure, PSI ...... 247.3 Base re1 a t i ve density .......... O. 7943 volume a t a l te rna te t & P ...... 1000

Input Data









KO ............................. 330.301000000000 K I ............................. 0.000000000000 K2 ............................. 0.000000000000 A .............................. 0.000003606302 B .............................. 2.000000000000 Rho60* ......................... 793.521270459968

using j e t fue l coe f f i c i en ts :


S t e D 5 - ca lcu la te temera ture cor rec t ion fac to r C t l del t a t' ......................... 25 .O06483322928 C t l ............................ 0.986832406683





volume a t base condit ions ...... 988.46 Density a t t & P, kg/cu m ...... 784.3590249208 Relat ive density a t t & P ...... 0.785131594410



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A P I MPMS 11.1.6.1 Customary Units, Example 5 A volume o f a re f ined product i s measured a t observed condit ions o f temperature and pressure. The base API i s known. ca lcu la te the volume a t base condit ions and cor rec t the base density t o an a l te rna te condi t i on.

Commodi t y ...................... General i zed Refined product t a l te rna te temperature, 'F .... 55.9 P a l te rna te pressure, PSI ...... 350 Base API g rav i t y ............... 48.0015 volume a t a l te rna te t & P ...... 10000

Input Data








step 3 - S h i f t Rho60 t o IPTS-68 temperature scale using t r a n s i t i o n zone coe f f i c i en ts :

KO ............................. 1.48906700000e+03 K I ............................. 0.000000000000 K2 ............................. -0.001868400000 A .............................. 0.000003661589 B .............................. 9.016112546440 Rho60* ......................... 787.521450184768


S t e D 5 - ca lcu la te temera ture cor rec t ion fac to r C t l del t a t' ......................... -4.101036330406 C t l ............................ 1.002182725702






A P I a t t & P .................. 47.2293336231



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A P I MPMS 11.1.6.1 Customary Uni ts, Example 6 A volume o f a re f i ned product i s measured a t observed condi t ions o f temperature and pressure. The base kg/m3 i s known. ca l cu la te the volume a t base condi t ions and cor rec t the base densi ty t o an a l te rna te condi t i on.

Commodi t y ...................... General i zed Refined product t a l te rna te temperature, 'F .... 27.3 P a l t e rna te pressure, PSI ...... 1234.5 Base dens i t kg/cu m .......... 657.3 volume a t ay iernate t & P ...... 14.72

Inpu t Data

computed Data - l a s t d i g i t i s rounded f o r d isp lay purposes

s tep 1 - check i npu t values f o r range excursion A l l i n p u t values w i t h i n range

Ca lcu la t ion o f volume co r rec t i on f a c t o r

s tep 2 - S h i f t temperature t t o IPTS-68 temperature scale t corrected t o IPTS-68 (t*> .... 27.298898616759


KO ............................. 192.457100000000 K i ............................. 0.243800000000 K2 ............................. 0.000000000000 A .............................. 0.000005612455 B .............................. 1.545657407721 Rho60* ......................... 657.303689061482

Step 4 - Determine c o e f f i c i e n t o f thermal expansion nlpha60 ........................ 0.000816362130

using gasol ine c o e f f i c i e n t s :

s tep 5 - ca l cu la te temperature co r rec t i on f a c t o r C t l d e l t a t ........................ -32.707976283241 C t l ............................ 1.026475833518

step 6 - ca l cu la te scaled compress ib i l i t y f a c t o r Fp FP f o r ps i ..................... 0.993527440282

step 7 - ca l cu la te pressure co r rec t i on f a c t o r cp l cp l ............................ 1.012417396817

step 8 - ca l cu la te the volume Correct ion Factor Ctpl Ctpl ........................... 1.039221991267 Ctp l , rounded .................. 1.03922

step 9 - ca l cu la te volume a t base condi t ions and densi ty a t a l te rna te condi t ions

volume a t base condi t ions ...... 15.2973184 Density a t t & P, kg/cu m ...... 683.0806148596



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A P I MPMS 11.1.6.1 Customary Uni ts, Example 7 A volume o f a specia l ized l i q u i d i s measured a t observed condi t ions o f temperature and pressure. The base r e l a t i v e densi ty i s known. ca l cu la te the volume a t base condi t ions and cor rec t the base densi ty t o an a l te rna te condi t i on.

Commodi t y ...................... Speci a l i zed L i qui d Alpha a t 6 0 ' ~ per ' F ........... 0.000732185 t a l te rna te temperature, ' F .... 97.7 P a l t e rna te pressure, PSI ...... 287.4 Base r e l a t i v e densi ty .......... 1.0537 volume a t a l t e rna te t & P ...... 203.85

Inpu t Data


Ca lcu la t ion o f In termediate Results

s tep 1 - check i npu t values f o r range excursion


A l l i n p u t values w i t h i n range


s tep 2 - S h i f t temperature t t o IPTS-68 temperature scale t corrected t o IPTS-68 (t*) .... 97.716729951690


Step 4 - Determine c o e f f i c i e n t o f thermal expansion Using user Alpha ............... 0.000732185000

S t e D 5 - ca l cu la te t e m e r a t u r e co r rec t i on f a c t o r C t l del t a t' ......................... 37.709855051690 C t l ............................ 0.972173795696

step 6 - ca l cu l ate scaled compressi b i 1 i t y f a c t o r FP f o r ps i ..................... 0.346454796729

step 7 - ca l cu la te pressure co r rec t i on f a c t o r cp cp l ............................ 1.000996703515

step 8 - ca l cu la te the volume Correct ion Factor Ctpl ........................... 0.97314276473s Ctp l , rounded .................. 0.97314


volume a t base condi t ions ...... 198.374589 Density a t t & P, kg/cu m ...... 1024.3915370787 Re la t i ve densi ty a t t & P ...... 1.025400531201

FP



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A P I MPMS 11.1.6.1 Customary Uni ts, Example 8 A volume o f a lube o i l i s measured a t observed condi t ions o f temperature and pressure. The base A P I i s known. ca l cu la te the volume a t base condi t ions and co r rec t the base densi ty t o an a l te rna te cond i t ion .

Commodi t y . . . . . . . . . . . . . . . . . . . . . . t a l te rna te temperature, 'F .... 129.3 P a l t e rna te pressure, PSI .. .... 138.8 Base API g r a v i t y ............... 42.9 volume a t a l t e rna te t & P .. .... 99.98

Inpu t Data General i zed Lube O i 1







s tep 2 - S h i f t temperature t t o IPTS-68 temperature scale t corrected t o IPTS-68 (t*) . . . . 129.325201088023

step 3 - S h i f t Rho60 t o IPTS-68 temperature scale KO ............................. 0.000000000000 K i ............................. 0.348780000000 K2 ............................. 0.000000000000 A .............................. 0.000002958254 B .............................. ~.oooooooooooo Rho60* ......................... 810.557237278501

Step 4 - Determine c o e f f i c i e n t o f thermal expansion nlpha60 ........................ 0.000430296571

step 5 - ca l cu la te temperature co r rec t i on f a c t o r C t l d e l t a t ........................ 69.318326188023 C t l ............................ 0.969922293864

step 6 - ca l cu la te scaled compress ib i l i t y f a c t o r Fp FP f o r ps i ..................... 0.732650236105

step 7 - ca l cu la te pressure co r rec t i on f a c t o r cp l cp l ............................ 1.001017953704

step 8 - ca l cu la te the volume Correct ion Factor Ctpl Ctpl ........................... 0.970909629855 Ctp l , rounded .................. 0.97091


volume a t base condi t ions . . . . . . 97.0715818 oensi ty a t t & P, kg/cu m ...... 786.9754991473

A P I a t t & P .................. 48.12 536845 58



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A P I MPMS 11.1.6.1 Customary Uni ts , Example 9 A volume o f a crude o i l i s measured a t observed condi t ions o f temperature and pressure. The base A P I i s known. c a l c u l a t e the volume a t base condi t ions and c o r r e c t the base densi ty t o an a l t e r n a t e condi t ion.

Commodity ...................... Generalized crude O i l t a l t e r n a t e temperature, 'F .... -58.05 P a l t e r n a t e pressure, PSI ...... O Base API g r a v i t y ............... 100 volume a t a l t e r n a t e t & P ...... 1000

I n p u t Data



s tep 1 - check i n p u t values f o r range excursion

Density kg/cu meter (Rho60) .... 610.629650107991

Temperature l e s s than -5O'C ( - 5 8 ' ~ ) - outs ide l i m i t s o f t a b l e


Commodity ...................... Generalized crude O i l t a l t e r n a t e temperature, 'F .... 302.05 P a l t e r n a t e pressure, PSI ...... O Base API g r a v i t y ............... 100 volume a t a l t e r n a t e t & P ...... 1000

I n p u t Data



s tep 1 - check i n u t values f o r range excursion


Temperature greater tRan 150'C ( 3 0 2 ' ~ ) - outs ide l i m i t s o f t a b l e


I n p u t Data Commodity ............... t a l te rna te temperature, P a l t e r n a t e pressure, PSI Base API g r a v i t y ........ volume a t a l t e r n a t e t & P

...... Generalized crude O i l F .... 92 ...... 1501 ...... 100 ...... 1000


Ca lcu la t ion o f In termediate Results Density kg/cu meter (Rho60) .... 610.629650107991

s tep 1 - check i n p u t values f o r range excursion Pressure greater than 1500 p s i - outs ide l i m i t s o f t a b l e



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API MPMS 11.1.6.1 customary u n i t s , Example 12 A volume o f a crude o i l i s measured a t observed condi t ions o f temperature and pressure. The base A P I i s known. c a l c u l a t e the volume a t base condi t ions and c o r r e c t the base densi ty t o an a l t e r n a t e condi t ion.

Commodity ...................... Generalized crude O i l t a l t e r n a t e temperature, ' F .... 72 P a l t e r n a t e pressure, PSI ...... O Base API g r a v i t y ............... 100.06 volume a t a l t e r n a t e t & P ...... 1000

I n p u t Data





Density l e s s than 610.6 kg/cu m - outs ide l i m i t s o f t a b l e

A P I MPMS 11.1.6.1 Customary Uni ts , Example 13 A volume o f a r e f i n e d product i s measured a t observed condi t ions o f temperature and pressure. The base API i s known. c a l c u l a t e the volume a t base condi t ions and c o r r e c t the base dens i ty t o an a l t e r n a t e condi t i on.

Commodi t y ...................... General i zed Refined product t a l t e r n a t e temperature, ' F .... 302 P a l t e r n a t e pressure, PSI ...... O Base API g r a v i t y ............... -10.08 volume a t a l t e r n a t e t & P ...... 1000

I n p u t Data





Density greater than 1163.5 kg/cu m - outs ide l i m i t s o f t a b l e

A P I MPMS 11.1.6.1 Customary Uni ts , Example 14 A volume o f a lube o i l i s measured a t observed condi t ions o f temperature and pressure. The base A P I i s known. c a l c u l a t e the volume a t base condi t ions and c o r r e c t the base densi ty t o an a l t e r n a t e condi t ion.

I n p u t Data Commodi t y ...................... General i zed Lube O i 1 t a l t e r n ä t e temperature, ' F .... O P a l t e r n a t e pressure, PSI ...... O Base API g r a v i t y ............... 45.08 volume a t a l t e r n a t e t & P ...... 1000





Density l e s s than 800.9 kg/cu m - outs ide l i m i t s o f t a b l e



--`,,`,,,-`-`,,`,,`,`,,`---

SECTION 1 - VOLUME CORRECTION FACTORS FOR CRUDE OILS, REFINED PRODUCTS, & LUBE OILS 45

API MPMS 11.1.6.1 customary u n i t s , Example 1 5 A volume of a crude o i l i s measured a t observed condi t ions o f temperature and pressure. known.

Commodity ...................... Generalized crude O i l t a l te rna te temperature, ' F .... 200 P a l te rna te pressure, PSI O Base API g r a v i t y 100 volume a t a l t e rna te t & P ...... 1000

The base API i s ca l cu la te the volume a t base condi t ions and co r rec t the base densi ty t o an a l te rna te cond i t ion .

I npu t Data

...... ...............


ca l cu la t i on o f In termediate Results


Density kg/cu mete r (Rho601 .... 610.629650107991


ca l cu la t i on o f volume co r rec t i on f a c t o r

s tep 2 - s h i f t temperature t t o IPTS-68 temperature scale

s tep 3 - S h i f t ~ h o 6 0 t o IPTS-68 temperature scale

t corrected t o IPTS-68 (t*> .... 200.043348977974

KO ............................. 341.095700000000

A .............................. 0.000006289074

Rho60* ......................... 610.633490386188

nlpha60 ........................ 0.000914776512

K I ............................. 0.000000000000 K2 ............................. 0.000000000000

B .............................. 2.000000000000

step 4 - Determine coef f i c ien t o f thermal expansion

s tep 5 - ca l cu la te temperature co r rec t i on f a c t o r c t l d e l t a t ........................ 140.036474077974 C t l ............................ 0.868288296907

step 6 - Calcu late scaled compress ib i l i t y f a c t o r FP

s tep 7 - ca l cu la te pressure co r rec t i on f a c t o r cp l

s tep 8 - Calcu late the volume Correct ion Factor Ctpl

FP f o r p s i ..................... 4.092820997603

cp1 ............................ 1.000000000000

Ctpl ........................... 0.868288296907 c t p l , rounded .................. 0.86829


volume a t base condi t ions ...... 868.29 oensi ty a t t & P, kg/cu m ...... 530.2025789330

A P I a t t & P .................. 135.116515303



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11.1.6.2 Method to Correct Volume and Density from Observed Conditions to Customary Base Conditions


This procedure calculates the density at the base conditions (60'F and O psig) that is consistent with an observed density at its temperature and pressure condition. The procedure has the flexibility of accepting a pre-calculated 60'F thermal expansion factor or calculating one based upon the commodity type of the liquid.

The equations for the temperature and pressure correction factors are direct functions of the base density. In this procedure, however, this base density is unknown. So, the base density must be calculated using iteration. This basic procedure is:

1) Estimate a value for the 60'F density.

2) Calculate the observed density via the procedure outlined in 1 1.1.6.1.

3) Compare this result with the given observed density.

4) If the calculated observed density is acceptably close to the given observed density, then the iterations are complete.

5) If the calculated and given observed densities are not acceptably close, then the value for the 60'F density is changed and we repeat the process, starting at step 2.

This final iterative value of the 60'F density is the desired output from this procedure.

A Newton's method of iteration procedure is outlined here. The Newton's method is a specific way to determine how the value for the 60'F density is changed in step 5 above. However, this method need not be used to comply with the implementation procedure. Other initial guesses or iterative solution techniques could be used and still be deemed compliant with this Standard provided the process is continued until the calculated and given observed densities are acceptably c l o s e this criterion is Step 4 of this procedure. See 11.1.3.5 and Appendix F for further discussions about this iteration scheme.

Note that when using the Generalized Refined Products group (the B Tables), the sub-group may change depending upon the iterative value of the base density, p60. This sub-group switching is automatically performed as part of this iteration procedure. Other iterative procedures may not be able to do this.

The calculation steps are depicted in Figure 1 1.1.6.2.A.


Input Values

Commodity group describing liquid (if cx60 not input)

cx60 Pre-calculated 60'F thermal expansion factor (if commodity group not given)

P O Observed density (kg/m3)

t0 Temperature at which the observed density was measured (OF)

P, Pressure at which the observed density was measured (psig)



--`,,`,,,-`-`,,`,,`,`,,`---



V,

Output Values

p60

CTL

CpL

Fp Scaled compressibility factor (psi-')

CTpL


V60

Intermediate Values

pg) Value of &o on the m-th iteration

&O,max Maximum value allowed for &o on any iteration

&O,mh Minimum value allowed for &o on any iteration

Volume at observed conditions (any valid set of units, such as barrels, liters, and cubic metres)

Density at base conditions (60'F and O psig) (kg/m3)

Volume correction factor due to temperature

Volume correction factor due to pressure

Combined volume correction factor due to temperature and pressure

Volume at base conditions (60'F and O psig) (same set of units as V )

C g ) Volume correction factor due to temperature on the m-th iteration

At

6pT)

Volume correction factor due to pressure on the m-th iteration

Value of the combined VCF due to temperature and pressure on the m-th iteration

Scaled compressibility factor on the m-th iteration (psi-')

Temperature difference from the base temperature of 60'F (OF)

Deviation between the value of the observed density po and the estimate of &o on the m-th iteration

Change applied to the value of pg) on the m-th iteration to get the value on the next iteration (kg/m3)

Coefficient needed to perform iteration on &o

Correction factor due to temperature used in iterative procedure

Correction factor due to pressure used in iterative procedure

Correction factor due to density used in iterative procedure



--`,,`,,,-`-`,,`,,`,`,,`---


Lubricating Oil


Stepl: Check the input values to determine if they are in the range of this Standard. The following are the valid limits:

-58.0°F < to < 302.0°F

O < Po < 1500 psig

pmin < po < pm, (if commodity type is specified)

230.0 x 10-6 OF-' < a 6 0 < 930.0 x 10-6 OF-' (if a 6 0 , not commodity type, is specified)

The following table gives the largest possible po limits for the various commodity groups. This check does not have to be done if a 6 0 , not the commodity group, is specified. Note that even if a po value is within these limits it may still not correspond to a valid p60 value.

714.3 kg/m3 1208.3 kg/m3

I Commodity Type I Pmin I Prnm I

Commodity Type

Crude Oil

Refined Products

Lubricating Oil

I Crude Oil I 470.5kg/m3 I 1201.8kg/m3 I

P60,min P60,max

6 10.6 kg/m3

800.9 kg/m3

1163.5 kg/m3

I Refined Products I 470.4kg/m3 I 1209.5 kg/m3 I

If any of the input variables are out of range set an error condition (such as setting all output values to zero) and exit procedure.

Step 2: Use the observed density po as the initial guess for the density at base conditions, pg)

Limit this initial guess to remain in the range of this Standard. Set:

Step 3: Following the procedure in 1 1.1.6.1 , calculate the correction factor due to temperature and pressure, C$l , using the current guess for the density at base conditions, pg). Do not check the input values for being in

the proper range. Do not round the value of C$l. Retain the value of am as ag' .



--`,,`,,,-`-`,,`,,`,`,,`---


Step 4: Determine if the result of this current estimate for the density at base conditions and the corresponding CTPL reproduces the observed density. If it does then the calculation has converged and the iterations should halt. The estimate is considered as “good enough” if:

18po)1< 0.000001 kg / m3 where 6po) = po - pg) . C g l .

If this condition is true, go to Step 7.

Step 5: Revise the estimate for the density at base conditions. The general recursion equation is:

Newton’s iteration method to determine Apg) is:

where:

The O?) values depend upon the commodity group and are obtained fiom the following table. If the cx60

value has been specified as an input value, then OF) = O (meaning that Op) = O). Note that when dealing with Generalized Refined Products the sub-group could change during the course of the iterations (depending on the current pi:) value) resulting in different O(“) values fiom one iteration to the next.

Refined Products (B)



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There are cases where the Newton’s method Apz) value should not be directly used:

o If the Newton’s method gives a value outside of the valid range for this Standard, constrain the Apz) value to go only to the boundary:

Step 6: Increment the iteration counter to m+ 1. If this value for the iteration counter is less than or equal to 15 continue the iterative procedure with Step 3. Otherwise set an error condition for non-convergence (such as setting all output values to zero) and exit procedure.

(Note: If the commodity class is Refined Products with a density near the boundary of a product group, there may be rare instances where convergence may fail due to a mathematical anomaly. In these instances, the resulting density should be within acceptable tolerance after 15 iterations. The density from the last iteration may be used to calculate the CTF’L and the result should be flagged with a note that it did not converge.. This resulting CTF’L should be within acceptable tolerance.)

Step 7: After the convergence criterion in Step 4 is met, set the value of p60 to the last pg) value and set the value

of C,,, to the last Cgl value. Check this p60 value to determine if it is in the range of this Standard. If p60 < p60,min or p60 > p60,max then this p60 value is out of range. Set an error condition (such as setting all output values to zero) and exit the procedure. Round this value of C,, consistent with 1 1.1.5.4.

Step 8: If volume V, has been input and the temperature and pressure for the density are the same as those for Voy the volume at base conditions is calculated:




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Figure 11.1.6.2.A Flow Chart Of Procedure For Correcting Volume and Density from Observed Conditions to Base Conditions

Set p a = pa@)

Enter v,, Po, to, Po,

Yes

Set p60(0) = p, Set m=û

c

No

Compute value of Ap 60(m)

No

-1 . Increment m to m+l

Adjust pa(o) 1

'I Adjust value of Ap 60(m)

m > 15? Flag error & Exit

Flag error & Exit

No . ~ Compute c,,, & va Exit \i



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Example Calculations

I n p u t Data Commodity ...................... Generalized crude O i l t observed temperature. ' F ..... 80.3 P observed pressure, PSI . . . . . . . - 5

Forcing negative pressure(s1 t o zero Dens, kg/cu m , observed t & P .. 823.7 volume a t observed t & P ... .... 1000


s tep 1 A l l i n p u t data w i t h i n range o f procedure

s tep 2 I n i t i a l densi ty , kg/cu m . . . . . . . 823.700000000000

I terat ion(m) . . . . . O 1 s t e

~hoóO(mY KO(m) . .. K1(M) . .. K2(m) . . . Atm) . . . .

..........

..........

..........

..........

..........

.......... a l ha60(m) . . . . . . . . . ct?(m) . . . . . . . . . . . . . -I - 1 - L - f - X U-dIc)lld<lllJ . . . . . . . . . Fp(m) .............. c p l (m) . . . . . . . . . . . . . c t p l (m) . . . . . . . . . . . . ~hoGO(m)xctpl (m) . . .

s tep 4 del t a ~ho6O(m) . . . . .

s tep 5 E(M) ............... Dt(m) .............. Dp(m) .............. d e l t a Rho(m) ... .... ~hoGO(m+l) .........

823.700000000000 832.047700405069 341.095700000000 341.095700000000

0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000003456244 0.000003387241 2.000000000000 2.000000000000

823.702846901034 832 .Ö50518744082 0.000502730357 0.000492693523 O. 9897612922 56 0.989966291106 2.000000000000 2.000000000000 0.583649345323 0.567047025149 1.000000000000 1.000000000000 O. 9897612922 56 o. 989966291106

815.266376431390 823.699175993020

8.433623568610 0.000824006980

8.520866227639 0.000832358624 O .O20744134812 0.020323464473

-0.000000000000 -0.000000000000 347700405068 0.000815779165 8.

832

s tep 6, i terat ion(m)

s tep 7 Density a t 60'F i s w i t h output values

Density a t 6 0 ' ~ . . . C t l FP f o r p s i ........ cp1 c tp1 Ctp l , rounded .....

volume a t base cond

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

s tep 8 t

...

047700405069 832 .o48516184234

.... 1 2

n range o f procedure

...... 832.048516184234 .......... 0.989966310837 .......... 0.567045450015 .......... 1.000000000000 .......... 0.989966310837 .......... 0.98997

ons ...... 989.97

2

832.048516184234 341.095700000000

0.000000000000 0.000000000000 0.000003387234

i. 000000000000 0.989966310837

823.700000004364

-0.000000004364



--`,,`,,,-`-`,,`,,`,`,,`---


Example 2 I n p u t Data

Commodity ...................... Generalized crude O i l t observed temperature, ' F ..... -57.95 P observed pressure, PSI ....... 113.5 Re1 densi ty , observed t & P .... O. 72332 volume a t observed t & P ....... 637483


Ca lcu la t ion o f In termediate Results Density kg/cu meter ............ 722.608253120000

s tep 1

step 2

A l l i n p u t data w i t h i n range o f procedure

I n i t i a l densi ty , kg/cu m ....... 722.608253120000

I terat ion(m) ..... O 1 2 3 Ste 3

Rho60 (my ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l pha60(m) ......... c t l (m) ............. d-al ha(m) ......... c p l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl (m) ...

Fp(& ..............

663.810409807890 341.095700000000

0.000000000000

663.445091139654 341.095700000000

0.000000000000

663.445062852402 341.095700000000

0.000000000000 0.000000000000 0.000004490934 2.000000000000

0.000000000000 0.000005321749 2.000000000000

0.000000000000 0.000005327611 2.000000000000

0.000000000000 O. 000005327612 2.000000000000

1.000541672744 1.000684240711 1.089080935549

722.943262140502

1.000685369796 1.000685369884 i. 075574910423

777.219307120433 i. ö89i757ii3ii

722.608279058022

..........

1.089175718656 722.608253120858

Ste 4 del t a RRo60(m) ..... -54.611054000433 -0.335009020502 -0.000025938022 -0.000000000858

s tep 5 E(M) ............... Dp(m) .............. Dt(m) .............. d e l t a Rho(m) ....... ~hoGO(m+l) .........

-50.773826603075 -0.135100362757 -0.001367511863

-0.307607092887 -0.155928968285 -0.002047013691

-0.000023814360 -0.156071317540 -0.002052650200

-58.797843312110 663.810409807890

-0.365318668236 663.445091139654

2

-0.000028287253 663.445062852402

3 s tep 6, i terat ion(m) ..... 1

step 7 Density a t 60'F i s w i t h i n range o f procedure output values

Density a t 6 0 ' ~ ................ 663.445062852402 Re la t i ve densi ty . . . . . . . . . . . . 0.664098535812

.......... 1.088429741690

.......... 0.603436540820

.......... 1.000685369884

t

C t l ............... FP f o r p s i ........ cp1 ............... ctp1 .............. Ctp l , rounded .....

volume a t base cond s tep 8

.......... 1.089175718656

.......... 1.08918

ons ...... 694333.73394



--`,,`,,,-`-`,,`,,`,`,,`---

SECTION 1 . VOLUME CORRECTION FACTORS FOR CRUDE OILS . REFINED PRODUCTS . & LUBE OILS 54

Example 3

t observed temperature. ' F ..... 68 P observed pressure. PSI ....... 11 Re1 densi ty . observed t & P .... O . 8665 volume a t observed t & P ....... 28.45

I n p u t Data Commodi t y ...................... General i zed Refined product



s tep 1

step 2


I n i t i a l densi ty . kg/cu m ....... 865.647364000000

I terat ion(m) ..... O 1 2 s tep 3

Commodity .......... f u e l o i l f u e l o i l f u e l o i l ~ho6O(m) ........... 865.647364000000 868.722758639837 868.722680008428 KO(m) .............. 103.872000000000 103.872000000000 103.872000000000 K1(M) .............. 0.270100000000 O .2 70100000000 O .2 70100000000 K2(m) .............. 0.000000000000 0.000000000000 0.000000000000 A(m)- ............... 0 . 000003098089 0.000003083760 0.000003083760 B(M) ............... 1.307601778625 1.306846968664 1.306846987915 ~hoGO*(m) .......... 865.650045852404 868.725437571840 868.725358940506 a l ha60(m) ......... 0.000450635987 0.000448551701 0.000448551754 ct?(m) ............. O . 996390100819 0.996406815126 0.996406814700 ddaiDha (m) ......... i . 300000000000 1.300000000000 1.300000000000 _ _ Fe(m j .............. o . 489197 52 13 74 0.484824153195 0.484824263921 Cpl(m) ............. 1.000053814623 1.000053333501 1.000053333513 Ctp l (m) ............ 0.996443721177 0.996459956990 0.996459956576 ~hoGO(m)xCtpl(m) ... 862.568880610988 865.647442710117 865.647363997967

s tep 4

s tep 5

d e l t a ~ho6O(m) ..... 3.078483389012 -0.000078710117 0.000000002033

E(M) ............... 3.089470407196 -0.000078989744 Dt(m) .............. 0.004713647310 O . O04691721251 Dp(m) .............. -0.000136749381 -0.000134568925 d e l t a Rho(m) ....... 3.075394639836 -0.000078631409 ~ho6O(m+l) ......... 868.722758639837 868.722680008428

s tep 6, i terat ion(m) ..... 1 2

s tep 7 Density a t 60'F i s w i t h i n range o f procedure output values

Density a t 6 0 ' ~ ................ 868.722680008428 Re la t i ve densi ty ............... 0.869578345100 C t l ............................ 0.996406814700 FD f o r Dsi ..................... 0.484824263921 Cpl ............................. 1.000053333513 Ctp l ........................... 0.996459956576 Ctp l , rounded .................. 0.99646

s tep 8 volume a t base condi t ions ...... 28.349287



--`,,`,,,-`-`,,`,,`,`,,`---


Example 4

Commodi t y ...................... General i zed Refined product t observed temperature. ' F ..... 72 P observed pressure. PSI ....... 375 A P I g r a v i t y . observed t & P .... 41.4 volume a t observed t & P ....... 200.5

I n p u t Data

computed Data - l a s t d i g i t i s rounded f o r d i sp lay purposes

Calcu lat ion o f Intermediate Resul ts Density kg/cu meter ............ 817.586836321573

step 1

step 2


I n i t i a l densi ty. kg/cu m ....... 817.586836321573

I terat ion(m) ..... 0 Steo 3 _ _ _ .

Commodi i y .......... j e t f u e l ~ho6O(m) ........... 817.586836321573 KO(m) .............. 330.301000000000 K i ( m j .............. 0 . oooooooooooo K2(m) .............. 0.000000000000

1

i e t f u e l

0.000003371617 A(m)- ............... 0 . 000003397100

~hoGO*(m) .......... 817.589613739330 820.673469683855 a l ha60(m) ......... 0.000494127651 0 . 000490421047

2.000000000000

B(M) ............... 2.000000000000 2: öööööööööööö

ct?(m) ............. 0 . 994058492860 0.994103138776

2

i e t f u e l

0.000003371618 2: öööööööööööö

820.673391112864 0 . 000490421141 0.994103137645 2.000000000000

Fe(mj .............. 0 . 578821088788 0.572609812544 0.572609969057 cp l (m) ............. 1.002175300745 1.002151907560 1.002151908149 Ctpl(m) ............ 0.996220869040 0.996242356836 0.996242356288 ~hoGO(m)xCtpl(m) ... 814.497068596135 817.586915046689 817.586836321334

step 4 d e l t a ~ho6O(m) ..... 3.089767725439 -0.000078725116 0.000000000239

step 5 E(M) ............... 3.101488 Dt(m) .............. 0.011971!

557244 -0.000079022053 573527 0.011880933438

D d m i .............. .o . 006257228682 -0.006143505500 d k ì t a Rho(m) ....... 3.083866381287 -0.000078571256 ~hoGO(m+l) ......... 820.670702702861 820.670624131605

step 6, i terat ion(m) ..... 1 2

s tep 7 Densi ty a t 60'F i s w i t h i n range o f procedure output values

Density a t 6 0 ' ~ ................ 820.670624131605 A P I g r a v i t y .................... 40.750303402271 C t l ............................ 0.994103137645 FD f o r Dsi ..................... 0.572609969057 Cpl ............................. 1.002151908149 Ctp l ........................... 0.996242356288 C tp l , rounded .................. 0.99624

step 8 volume a t base condi t ions ...... 199.74612



--`,,`,,,-`-`,,`,,`,`,,`---


Example 5

Commodi t y ...................... General i zed Refined product t observed temperature. ' F ..... 25.3 P observed pressure. PSI ....... 267 Dens. kg/cu m. observed t & P .. 803.141 volume a t observed t & P ....... 9998.7

Input Data


step 1

step 2

A l l i npu t data w i th in range o f procedure

I n i t i a l density. kg/cu m ....... 803.141000000000

Iterat ion(m) ..... O step 3

commodity .......... ~ho6O(m) ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) ......... ct?(m) .............

cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl (m) ...

d-al pha(m) ......... Fp(m) ..............

step 4 del t a ~ho6O(m

step 5 E(M) ........ Dt(m) ....... Dp(m) ....... de l ta Rho(m) . ~hoGO(m+l) ...

.....

......

......

......

......

......

j e t fue l 803.141000000000 330.301000000000

0.000000000000 0.000000000000 0.000003520404 2.000000000000

803.143827374024 0.000512062812 1 . 017674681289 2.000000000000 O . 512082157017 1.001369131317 1.019068011565

818.455301876645

-15.314301876645

-15.027752517833 ...............

-0.034526847401 -0.003620114436

-15.623751156981 787.517248843019

1 2 3

t rans i t i on 787.517248843019

1.48906700000e 0.000000000000

-0.001868400000 0.000003661644 9.016006690076

787.520132369253 0.000532593084 1.018379066764 8.500000000000 0.539941779272 1.001443725890 1.019849326989

803.148936224643

-0.007936224643

-0.007781761906

step 6. i terat ion(m) ..... 1

step 7 Densitv a t 60'F i s w i th in range o f procedure output- values

Density a t 6 0 ' ~ ...... C t l ................. FP f o r ps i .......... cp1 ................. ctp1 ................ Ctpl . rounded .......

volume a t base condi t step 8

.......... 787.507922593917

.......... 1.018381017381

.......... 0.539959363768

.......... 1.001443772976

.......... 1.019851328373

.......... 1.01985

ons ...... i0197 . 174195

t rans i t i on 787.508024225311

+O3 1.48906700000e4 0.000000000000

-0.001868400000 0.000003662031 9.015265799128

787.510908022297

-03

t rans i t i on 787.507922593917

1.48906700000e+03 0.000000000000

-0.001868400000 0.000003662035 9.015257637156

787.510806393886 0.000532649331 0.000532649951 1.018380996124 1.018381017381 8.500000000000 8.500000000000 0.539959172137 0.539959363768 1.001443772463 1 . 00 1443 7 72 9 76 1. 019851306563 1.019851328373

803.141087435169 803.141000961936

-0.000087435169 -0.000000961936

-0.000085733252

-. L 3



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i zed Refined product t observed temperature. ' F ..... 139 P observed pressure. PSI ....... 100 Re1 densi ty . observed t & P .... O . 7322 volume a t observed t & P ....... 1000

computed Data . l a s t d i g i t i s rounded f o r d isp lay purposes


s tep 1

step 2


I n i t i a l densi ty . kg/cu m ....... 731.479515200000

I terat ion(m) ..... Steo 3

0 1 2 3

KO(m) .............. 192.457100000C K1(M) .............. 0.243800000000 K2(m) .............. 0.000000000000 -0.001868400000 0.000000000000 0.000000000000 Atm) ............... 0.000004764222 0.000004405447 0.000004405346 0.000004405351 B i m j ............... 1 . 519ö43562955 7.831444710641 1.5Ö61Ö8416142 1.5Ö61Ö86Ö6983 ~hoGO*(m) .......... 731.483000127510 770.355595657728 770.353776055661 770.353187910199 a l ha60(m) ......... 0.000692983108 0.000640779647 0.000640782868 0.000640783604

ddalDha(m) ......... 1.500000000000 8.500000000000 1.500000000000 1.500000000000 ct?(m) ............. 0 . 944443401311 0.948677400428 0.948677139402 0.948677079691 _ _ Fe(mj .............. 1 . 118639209920 0.910912736669 O . 910920838482 O . 91092 345 72 38 c p l (m) ............. 1.001119891965 1.000911743255 1.000911751372 1.000911753995 Ctpl(m) ............ 0.945501075887 0.949542350649 0.949542097086 0.949542039808 ~hoGO(m)xCtpl(m) ... 691.614668611132 731.482040724130 731.480117593762 731.479515000034

s tep 4

s tep 5

d e l t a ~ho6O(m) ..... 39.864846588868 -0.002525524130 -0.000602393762 0.000000199966

E(M) ............... 42.162666553771 -0.002659727740 -0.000634404481 Dt(m) .............. 0.089311509196 0.465134152690 0.082082941045 Dp(m) .............. -0.004676769130 -0.003432954458 -0.003433001237 d e l t a Rho(m) ....... 38.872686809943 -0.001819611110 -0.000588146773 ~ho6O(m+l) ......... 770.352202009943 770.350382398833 770.349794252060

s tep 6. i terat ion(m) ..... 1 2

s tep 7 Density a t 60'F i s w i t h i n range o f procedure output values

Density a t 6 0 ' ~ ................ 770.349794252060 Re la t i ve densi ty ............... 0 . 771108565080 C t l ............................ 0.948677079691 FD f o r Dsi ..................... 0.910923457238 Cpl ............................. 1.000911753995 Ctp l ........................... 0.949542039808 c t p l , rounded .................. 0.94954

3

s tep 8 volume a t base condi t ions ..... 949.54



--`,,`,,,-`-`,,`,,`,`,,`---


Example 7 Input Data

Commodity ...................... Alpha a t 6 0 ' ~ per ' F ........... t observed temperature. ' F ..... P observed pressure. PSI ....... Dens. kg/cu m. observed t & P .. volume a t observed t & P .......

Special i zed 1 0.00057634

84.5 573

853.7 5000

i qui d

computed Data . l a s t d i g i t i s rounded f o r display purposes

step 1

step 2



~hoGO(m7 ........... 853.700000000000 863.404788404903 863.403098613648

Iterat ion(m) ..... O 1 2 S t e 3

Rho60G(m) .......... 853.703382614631 863.408209472807 863.406519674857 ctl(m) 0.985817857839 0.985817857839 0.985817857839 d-alpha(m) ......... 0.000000000000 0.000000000000 0.000000000000 Fp(m) .............. 0.535641758165 O . 519613454257 0.519616156675 CDl(m) ............. 1.003078676432 1.002986276388 1.002986291965

.............

cipi(m) ............ o . 988852872044 0.988761782431 0.988761797787 ~hoGO(m)xCtpl(m) ... 844.183696864341 853.701657542469 853.700000000354

step 4 de l ta ~ho6O(m) ..... 9.516303135659 -0.001657542469 -0.000000000354

step 5 E(M) ............... 9.623578395423 -0.001676382015 Dt(m) .............. 0.000000000000 0.000000000000 Dp(m) .............. -0.008368035045 -0.007935441615 de l ta Rho(m) ....... 9.704788404903 -0.001689791254 ~ho6O(m+l) ......... 863.404788404903 863.403098613648

step 6, i terat ion(m) ..... 1 2

step 7 Density a t 60'F i s w i th in range o f procedure output values

Density a t 6 0 ' ~ ................ 863.403098613648 C t l ............................ 0.985817857839 FP f o r ps i ..................... 0.519616156675 cp l ............................ 1.002986291965 Ctpl ........................... 0.988761797787 Ctpl , rounded .................. 0.98876

volume a t base condit ions ...... 4943.8 step 8



--`,,`,,,-`-`,,`,,`,`,,`---


Example 8

Commodi t y ...................... General i 1 zed Lube O i t observed temperature. ' F ..... 78.7 P observed pressure. PSI ....... 12 8 A P I g rav i ty . observed t & P .... 23.6 volume a t observed t & P ....... 2 SOO

Input Data


Calculat ion o f Intermediate Results Density kg/cu mete r ............ 911.416918117344

step 1

step 2



Iterat ion(m) ..... O S t e 3

Rho60 (my ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l pha60(m) ......... c t l (m) ............. d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl (m) ...

Fp(& ..............

S t e 4 del t a RRo60(m) .....

step 5 E(M) ............... Dp(m) .............. Dt(m) .............. de l ta Rho(m) ....... ~hoGO(m+l) .........

0.000002630878 1.000000000000

1.000570889885 ..............

0.993393703061 905.395827320613

6.021090796731

6.061132437402 0.007238011198

-0.001342864386 6.025610578411

917

step 6. i terat ion(m)

step 7 Density a t 60'F i s w i th output values

Density a t 6 0 ' ~ ......... . _ _ API g rav i t y ....... -*-I L L I ............... FP f o r ps i ........ cp1 ............... ctp1 .............. Ctpl . rounded .....

volume a t base cond step 8

t

...

....

....

....

442528695754

.... 1

1

917.442528695754 0.000000000000 0.348780000000 0.000000000000 0.000002613599 1.000000000000

917.444926524466 0.000380164509 0.992874117241 1.000000000000 0.438941834085 1.000562161396 0.993432272740

911.417016390699

-0.000098273355

-0.000098923055 0.007189938664

-0.001305020283 -0.000098344306

917.442430351448

2


...... 917.442430351448

...... 22.581345404799

...... 0.992874116475

...... 0.438941943315

...... 1.000562161535 .......... 0.993432272113 .......... 0.99343

ons ...... 2483.575

2

0.000002613599 1.000000000000

1.000562161535 0 . 993432272113

911.416918117159

0.000000000185



--`,,`,,,-`-`,,`,,`,`,,`---


Example 9

Commodi t y ...................... General i 1 zed Lube O i t observed temperature. ' F ..... 302 P observed pressure. PSI ....... 1499.97 A P I g rav i ty . observed t & P .... 62 volume a t observed t & P ....... 989.4

Input Data


Calcu lat ion o f Intermediate Results Density kg/cu meter ............ 730.546583979328

step 1

step 2


I n i t i a l densi ty. kg/cu m ....... 730.546583979328

Note. Rho60 has been l i m i t e d t o the minimum t a b l e value i n one o r more cases . Iterat ion(m) ..... 0

s tep 3 ~ho6O(m) ........... KO(m) .............. K i i m j .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) ......... ct?(m) ............. d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl (m) ...

del t a RRo60(m) .....

Fp(& ..............

Ste 4

s tep 5 E(M) ............... Dp(m) .............. Dt(m) .............. d e l t a Rho(m) ....... ~hoGO(m+l) .........

800.900000000000 0.000000000000 0.348780000000 0.000000000000 0: 000002993915 1.000000000000

800.902397828986 0.000435483775 0 . 891989089232 1.000000000000 ..............

1.460680703550 1.022400563598 0.911970147554

730.396891176188

0.149692803140

0 . 164142218407 0.123157370141

-0.104513388078 0: 161137965076

801 061137965076

step 6. i terat ion(m)

s tep 7 Density a t 60'F i s w i t h output values

Density a t 6 0 ' ~ . . . . . . . .... ....

API g r á v i t y ........ C t l ................ FP f o r ps i ........ cp1 ............... ctp1 .............. Ctp l . rounded .....

volume a t base cond s tep 8

... .. ..

t

.... 1

1

801.061137965076 0.000000000000 0.348780000000 0.000000000000

2

801.061124838869 0.000000000000 0.348780000000 0.000000000000

0.892011193142 1.000000000000 1 : 4 5 93 i047892 8 1.022379079982 0.911973582978

730.546596174628

-0.000012195300

-0.000013372427

-0.104371150492 -0.000013126207

0.123129022550

801.061124838869

2


...... 801.061124838869

...... 44.966888252047

...... 0.892011191342 .......... 1.459310590459 .......... 1.022379081731 .......... 0.911973582698 .......... 0.91197

ons ...... 902.303118

1.000000000000 1.459310590459 1.022379081731 0.911973582698

730.546583979040

0.000000000288



--`,,`,,,-`-`,,`,,`,`,,`---


Example 10

Commodity ...................... Generalized crude O i l t observed temperature, ' F ..... -58.05 P observed pressure, PSI ....... O A P I g rav i ty , observed t & P .... 169.16 volume a t observed t & P ....... 1000

Inpu t Data



observed temperature less than -5O'C (-58'~) - outside l i m i t s o f t a b l e Density less than 470.4 kg/cu m - outside l i m i t s o f tab le

s tep 1


Commodity ...................... Generalized crude O i l t observed temperature, ' F ..... 302.08 P observed pressure, PSI ....... 1500.12 A P I g rav i ty , observed t & P .... -13.88 volume a t observed t & P ....... 1000



observed temperature greater than 150'C (302'~) - outSide l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1201.8 kg/cu m - outside l i m i t s o f t a b l e

s tep 1

Example 12 Inpu t Data

Commodi t y ...................... General i zed Refined product t observed temperature, ' F ..... -58.05 P observed pressure, PSI ....... O Dens, kg/cu m, observed t & P .. 470.17 volume a t observed t & P ....... 1000


s tep 1 observed temperature less than -5O'C (-58'~) - outside l i m i t s o f t a b l e Density less than 470.3 kg/cu m - outside l i m i t s o f tab le


Commodi t y ...................... General i zed Refined product t observed temperature, ' F ..... 302.08 P observed pressure, PSI ....... 1500.05 Dens, kg/cu m, observed t & P .. 1209.52 volume a t observed t & P ....... 1000


s tep 1 observed temperature greater than 150'C (302'~) - outSide l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1209.5 kg/cu m - outside l i m i t s o f t a b l e



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i zed Lube O i 1 t observed temperature, ' F ..... 60 P observed pressure, PSI ....... O A P I g rav i ty , observed t & P .... -14.53 volume a t observed t & P ....... 1000



step 1 Density greater than 1163.5 kg/cu m - outside l i m i t s o f t a b l e

Example 15

Commodi t y ...................... General i zed Lube O i 1 t observed temperature, ' F ..... 72.32 P observed pressure, PSI ....... O A P I g rav i ty , observed t & P .... 66.48 volume a t observed t & P ....... 1000

Inpu t Data



Density less than 714.3 kg/cu m - outside l i m i t s o f tab le s tep 1


Commodi t y ...................... General i zed Lube O i 1 t observed temperature, ' F ..... -57.97 P observed pressure, PSI ....... 240.7 A P I g rav i ty , observed t & P .... -14.51 volume a t observed t & P ....... 1000



Density greater than 1208.3 kg/cu m - outside l i m i t s o f tab1 s tep 1



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.6.3 Method to Correct Volume and Density from Observed Conditions to Alternate Conditions


This procedure combines those in 1 1.1.6.2 and 1 1.1.6.1. First, the density at the base conditions (60'F and O psig) consistent with an observed density is calculated. This base density is then corrected to the alternate temperature and pressure conditions.


Input Values

Commodity group describing liquid (if cx60 not input)

a 6 0 Pre-calculated 60'F thermal expansion factor (if commodity group not given)


t0 Temperature at which the observed density was measured (OF)

P, Pressure at which the observed density was measured (psig)

t

P


Alternate temperature at which density is desired (OF)

Alternate pressure at which density is desired (psig)

V, Volume at observed conditions (any valid set of units, such as barrels, liters, and cubic metres)

Output Values

P Density at alternate conditions t and P (kg/m3)

P60 Density at base conditions 60'F and O psig (kg/m3)

CTL,o Volume correction factor due to temperature between the base and observed temperatures

CpL,o Volume correction factor due to pressure between the base and observed pressures at the observed temperature

Scaled compressibility factor at the observed temperature (psi-') FP,,

CTpL,o Combined volume correction factor due to temperature and pressure between the base and observed conditions

CTL Volume correction factor due to temperature between the base and alternate temperatures

CpL Volume correction factor due to pressure between the base and alternate pressures at the alternate temperature



--`,,`,,,-`-`,,`,,`,`,,`---


Fp Scaled compressibility factor at the alternate temperature (psi-')

CTpL Combined volume correction factor due to temperature and pressure between the base and alternate conditions


V Volume at alternate conditions t and P (same units as V , )

Go Volume at base conditions 60°F and O psig (same units as V , )


Step 1: Use the observed values po, to , and Po and determine the density at base conditions, , using the procedure in 11.1.6.2. If this procedure returns with an error condition, exit this procedure. Retain the values of CTL,o , FP,, , CpL,o , and CTpL,o in the procedure. Round this value of CTpL,o.

Step 2: With the p60 value found in Step 1, calculate the corresponding p density value at alternate conditions t and P using the procedure in 1 1.1.6.1. If this procedure returns with an error condition, exit this procedure. Retain the values of CTL , Fp , CpL , and CTpL in the procedure. Round this value of CTpL .

Step 3: Calculate the volumes at the base conditions:

and at the alternate conditions t and P:




--`,,`,,,-`-`,,`,,`,`,,`---




Commodity ...................... Generalized crude O i l t observed temperature. 'F ..... 80.25 t a l t e r n a t e temperature. 'F .... -57.9 P observed pressure. PSI ....... - 5 P a l t e r n a t e pressure. PSI ...... O

Forcing negative pressure(s1 t o zero Rho. observed dens i ty .......... 823.7 volume a t observed t & P ....... 1000


s tep 1

Correct ing observed dens i ty t o 60 'F & O p s i reference condi t ions:

I te ra t ion ím) ..... O ~ho6O(m) ........... KO(m) ..............

1 2

K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) ......... ct?(m) ...... d-alpha(m) . . c p l (m) ...... c t p l (m) ..... Rho60 (m) x c t p l del t a ~ho6O(m

Fp(m) .......

E(M) ........ Dt(m) ....... Dp(m) ....... d e l t a Rho(m) ~hoGO(m+l) . .

.......

.......

....... ...... ...... m) ... .....

......

......

......

......

......

'8~3.70000Ö000000 832 . 02729Ö281072 832 . O28099977475 341.095700000000 341.095700000000 341.095700000000

0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000003456244 0.000003387407 0.000003387400 2.000000000000 2.000000000000 2.000000000000

0.583545365081 0.566987343326 0.566985780172 1.000000000000 1.000000000000 1.000000000000 ..............

0.989786584353 0 . 989990582976 0 . 989990602513 815.287209531590 823.699182157009 823.700000004321

8.412790468410 0.000817842991 -0.000000004321 8.499600420336 0.000826111889 0.020692222013 0 . 020273630412 -0.000000000000 -0.000000000000 8.327290281072 0. 000809696404

832.027290281072 832.028099977475 output values

Rho60 ..................... C t l . o ..................... cp1. o ..................... ctp1. o .................... Fp. O ......................

c t p l .O. rounded ........... s tep 2

Correct ing 60'F and O p s i ... F .

t. 'F ......... t corrected t o

Rho60* ........ a l ha60 ....... C t l ........... Fp. p s i ......... P i n p s i .......

A ............. B .............

de?ta t. ...

CD1 ............

i

..

..

..

..... 5-68 ..... ..... ..... ..... ..... ..... ...... ...... ......

...

...

...

... C i p l ...................... c t p l . rounded ............. Density a t t & P. kg/cu m .

s tep 3 volume a t base condi t ions . volume a t a l t e r n a t e t & P .

..... 832.028099977475

..... 0.989990602513

..... 0 . 566985780172

..... 1.000000000000

..... 0.989990602513

..... 0 . 98999

densi t ..... ..... .... .... .... ..... ..... ..... .... .... .... ..... ..... .....

:y t o a l t e r n a t e Ca -57.900000000000 -57.917345475911

0.000003387400 2.000000000000

832.030918382881 0.000492716736

.11 7.924220375911 1.056966235844 0.349850873727 0.000000000000 1.000000000000 1.056966235844 1.05697

879.425608949795

..... 989.99

..... 936.630178718

indi t i o n s :



--`,,`,,,-`-`,,`,,`,`,,`---



Commodity ...................... Generalized crude O i l t observed temperature. ' F ..... -57.95 t a l te rna te temperature. ' F .... 301.95 P observed pressure. PSI ....... 113.5 P a l te rna te pressure. PSI ...... 1342 Rho. observed re1 density ...... 0 . 7233 volume a t observed t & P ....... 9988.7



step 1

Correcting observed density t o 60 ' F & O ps i reference condit ions:

I terat ion(m) ..... O 1 2 ~ho6O(m) ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) ......... ct?(m) ............. d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl (m) ... del t a ~ho6O(m) ..... Dt(m) .............. de l ta Rho(m) .......

Fp(& ..............

E(M) ............... Dp(m) .............. ~ho6O(m+l) .........

3 '722.588272800000 663.788670139111 663 -423300413573 663 -423272118035 ~~ _ _ _ ~ ....... 341.095700000000 341.0957OÖÖÖÖÖÖÖ 341.0957ÖÖOÖÖÖOÖ 341.0957OÖÖÖÖÖÖÖ

0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000004491182 0.000005322097 0.000005327961 0.000005327962 2.000000000000 2.000000000000 2.000000000000 2.000000000000

722.591518065349 663.792202873887 663.426835093931 663.426806798544 0.000653266707 0.000774126529 0.000774979431 0.000774979497 1.074996632822 1.088341810579 1.088435315140 1.088435322387 2.000000000000 2.000000000000 2.000000000000 2.000000000000 0.477019634140 0 . 602502062133 0.603495823943 0.603495901031 1.000541710576 1.000684307797 1.000685437263 1.000685437350 1.075578969868 1.089086571366 1.089181369263 1.089181376610

-0.001367683008 -0.002047348489 -0.002052987115 -58.799602660889 -0.36'5369725538 -0.000028295538 663.788670139111 663.423300413573 663.423272118035

output values Rho60 .......................... 663.423272118035

cp l . o .......................... 1.000685437350 c t p l . o ......................... 1.089181376610 c tp l .0 . rounded ................ 1.08918

C t l . o .......................... 1.088435322387 Fp. O ........................... 0.603495901031

step 2 Correctina 6 0 ' ~ and O mi densitv t o a l te rna te condit ions:

t. ' F .......................... A .............................. B .............................. t corrected t o IPTS-68 ' F ......

Rho60* ......................... alpha60 ........................ de l ta t. ' F .................... C t l ............................ Fp. ps i ......................... P i n ps i ....................... cp1 ............................ ctp1 ........................... c t p l . rounded .................. Density a t t & P. kg/cu m ......

volume a t base condit ions ...... volume a t a l te rna te t & P ......

step 3

+03

0 . 85467 567.009178129011

10879.492266 12729.4654849



--`,,`,,,-`-`,,`,,`,`,,`---

SECTION 1 . VOLUME CORRECTION FACTORS FOR CRUDE OILS, REFINED PRODUCTS. & LUBE OILS 67


Commodi t y ...................... General i zed Refined Product t observed temperature. 'F ..... 68.02 t a l t e r n a t e temperature. 'F .... 150.3 P observed pressure. PSI ....... 11 P a l t e r n a t e pressure. PSI ...... 5 34 Rho. observed re1 densi ty ...... 0.8665 volume a t observed t & P ....... 285.45



s tep 1


I t e r a t i o n Commodity .......... Rho60(m) ........... Kû(m) .............. Kï(m) .............. Kï(m) .............. A(m) ............... B(M) ............... Rho60*(m) .......... a l pha60(m) ......... . . c t i (m) ............. d-al ha(m) ......... Cpl (m) ............. Fp(my .............. Ctp l (m) ............ Rho60(m)xctpl (m) ... del t a ~ho6O(m) ..... _ _ E(M) ...............

(m) ..... O fi iol n i l .......

865.647364000000 103.872000000000

0.270100000000 0 . 000000000000 0.000003098089 1.307601778625

865.650045852404 0.000450635987 0.996381066426 1.300000000000 ..............

0.489229213867 1.000053818110 0.996434689772

862.561062599229

1 1

f u e l o i l 868.730560425361 103.872000000000

0.270100000000 ö öööööööööööö 0.000003083723 1.306845058542

868.733239349982 0.000448546437 0.996397864928 Ö . 996397864500 1.300000000000 1.300000000000 0.484844362415 0.484844473663 1.000053335724 1.000053335737 0.996451008530 0.996451008114

865.647443076884 865.647363997953 3.086301400771 3.097344394420

~ ~~

-0.000079076884 0 . 000000002047 -0.000079358527

Dt(ÏÏl) .............. Ö . ÖÖ472549918Ö O . 004703462163 Dp(m) .............. -0.000136764923 -0.000134578693 d e l t a Rho(m) ....... 3.083196425361 -0.000078997596 Rho60(m+l) ......... 868.730560425361 868.730481427765

output va1 ues Rho60 ..................... Fp. O ..................... C t l . o .................... cp1 o .................... c t p i .o ................... Ctp l .O. rounded ..........

Correct ing 6 0 ' ~ and O ps s tep 2

.....

.....

.....

.....

.....

.....

dens t. 'F .......................... t corrected t o IPTS-68 'F ...... A .............................. B .............................. Rh060" ......................... a l ha60 ........................ dePta t. 'F .................... C t l ............................ Fp. p s i ......................... P i n p s i ....................... cp1 ............................ ctp1 ........................... Ctp l . rounded .................. Density a t t & P. kg/cu m ......

s tep 3 volume a t base condi t ions ...... volume a t a l t e r n a t e t & P ......

868.730481427765 ~~

0.996397864500 0.484844473663 1.000053335737 0 . 996451008114 0 . 99645

t y t o a l t e r n a t e con 150.300000000000 150.330786371419

0.000003083724 1.306845077883

868.733160352460 0.000448546490

90.323911471419 0.959034901244 0.631776484622

534.000000000000 1.003385106716 0.962281336729 0 . 96228

835.963128925946

284.4366525 29S.586162551

id i t i o n s :



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i zed Refined product t observed temperature. 'r ..... 72.04

P a l te rna te pressure. PSI ...... 47.75 Rho. observed A P I g rav i t y ...... 41.4 volume a t observed t & P ....... 14.95

t a l te rna te temperature. F .... -58 P observed pressure. PSI ....... 375



step 1

Correcting observed density t o 60 'F & O ps i reference condit ions:

I terat ion(m) ..... 0 Commodity .......... ~ho6O(m) ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l pha60(m) ......... c t l (m) ............. d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl (m) ... del t a ~ho6O(m) ..... Dt(m) ..............

Fp(& ..............

E(M) ...............

1.002175615991 0 . 996201299764

814.481069013354 3.105767308219 3.117610174726 0.012011855055

2.000000000000

1.002152097771

_ _ DD(m) .............. -0.006258741122 -0.006144404888 ...... ~~~~

dé ì tá Rho(m) ....... 3.099776805597 .ö . 000079162951 ~hoGO(m+l) ......... 820.686613127170 820.686533964218

Rho60 .......................... 820.686533964218 Ct1.o .......................... 0.994083677273

output values

Fp. Ó ........................... 0 . 572660475665 cp l . o .......................... 1.002152098365 c t p l . o ......................... 0.996223043130 Ctpl.0. rounded ................ 0.99622

S t e D 2 Correkting 6 0 ' ~ and O ps i density t o a l te rna te condit ions:

t. F .......................... -58.000000000000 t corrected t o IPTS-68 'F ...... -58.017359639581 A .............................. 0.000003371487 B .............................. 2.000000000000 Rho60* ......................... 820.689300891838 a l ha60 ........................ 0.000490402127 de?ta t , O F .................... -118 . 024234539581 C t l ............................ 1.056751557035 Fp. ps i ......................... 0.359117236149 P i n ps i ....................... 47.750000000000 CD1 ............................ 1.000171507890 c i p l ........................... 1.056932798265 Ctpl . rounded .................. 1.05693 Density a t t & P. kg/cu m ...... 867.410514841381

1.002152098365 0. 996223043130

817.586836321331 0.000000000242

step 3 volume a t base condit ions ...... 14.893489 volume a t a l te rna te t & P ...... 14 . 0912728374



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i zed Refined product t observed temperature. 'r ..... 35.34 t a l te rna te temperature. F .... 127.98 P observed pressure. PSI ....... 38.4 P a l te rna te pressure. PSI ...... 121.8 Rho. observed density .......... 790.53 volume a t observed t & P ....... 99998


step 1


I terat ion(m) ..... O 1 2 3 Commodity .......... j e t fue l t rans i t i on t rans i t i on t rans i t i on ~ho6O(m) ........... 790.530000000000 779.954265918190 779.174329912980 779.174880755919 KO(m) .............. 330.301000000000 1.48906700000e+03 1.48906700000e+03 1.48906700000e+03 K i i m j .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l pha60(m) ......... c t l (m) ............. d-al ha(m) ......... Fp(& .............. cp l (m) ............. c t p l (m) ............ RhoGO(m)xct~l (m) ...

0.000000000000 0.000000000000 0.000003633619 2.000000000000

790.532872477731 0.000528530459 1.012984460926 2.000000000000 0.555420998123 1.000213327162 1.013200558026

800.965437136296

0.000000000000 -0.001868400000 0.000003983317 8.449428366970

779.957372634827 0.000579380687 1. 014228023715 8.500000000000 0.577092033703 1.0002 2 16 5 2460 1.0144528298 5 1

791.2 268122 15287

0.000000000000 -0.001868400000 0.000004017024 8.395311744142

779.177459785401 0.000584283321 1. 014347865394 8.500000000000 0 . 578759095821 1.000222292896 1 . 0 14 5 7 3 347 7 18

790.529508355868

0.000000000000 -0.001868400000 0.000004017000 8.395349701311

779.178010611977 0.000584279853 1.014347780630 8.500000000000 0.578757914964 1.000222292442 1.014573262475

790.530000807356 de l ta '~ho60 imj ..... -10.435437136296 -0.696812215287 0.000491644132 -0.000000807356 E(M) ............... -10.299478275680 -0.686884786342 o . 000484582147 Dt(m) .............. -0.025523526372 -0.118667770827 -0.119648229356 Dp(m) .............. -0.000598140833 -0.000638452051 -0.000641579262 de l ta Rho(m) ....... -10.575734081810 -0.779936005211 0.000550842939 RhoGO(m+l) .......... 779.954265918190 779.174329912980 779.174880755919

Rho60 .......................... 779.174880755919 C t l , o .......................... 1.014347780630

cp l , o .......................... 1.000222292442 c t p l . o ......................... 1.014573262475 Ctpl.0. rounded ................ 1.01457

output values

Fp, O ........................... 0.578757914964

step 2 Correcting 6 0 ' ~ and O ps i density t o a l te rna te condit ions:

t. F .......................... 127.980000000000

A .............................. B .............................. t corrected t o IPTS-68 'F ...... 128.004847502107

Rho60* ......................... a l ha60 ........................ C t l ............................ Fp. ps i ......................... 0.835760463789 P i n ps i ....................... 121.800000000000 cp l ............................ 1.001018993536 Ctpl ........................... 0.960814040896 Ctpl . rounded .................. 0.96081 Density a t t & P. kg/cu m ...... 748.642165743914

volume a t base condit ions ...... 101454.97086 volume a t a l te rna te t & P ...... 105593.167078

de?ta t. ....................

step 3



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i zed Refined product t observed temperature. 'r ..... 74.33 t a l t e r n a t e temperature. F .... . 50 P observed pressure. PSI ....... 2 P a l te rna te pressure. PSI ...... -2.33

Forcing negative pressure(s1 t o zero Rho. observed dens i ty .......... 602.6 volume a t observed t & P ....... 501.7


s tep 1


Note. Rho60 has been l i m i t e d t o the minimum t a b l e value i n one o r more cases . I terat ion(m) ..... 0 1 2

commodi t v .......... oasol i ne oasol i ne oasol i ne Rho6Ö(m)' ........... 610.6ÖÖÖ000Ö0000 610.620823885543 610.62Ö8063l0613 Kû(m) .............. 192.457100000000 192.457100000000 192.457100000000 Kl(m) .............. 0.243800000000 0.243800000000 0.243800000000 Ki(m) .............. 0.000000000000 0.000000000000 0.000000000000 A(m)- ............... 0 . 000006293846 0.000006293511 0.000006293511

............... 1.563858906231 1.563850519437 1.563850526515

c t l (m) ............. 0 . 986827537723 d-al ha(m) ......... 1.5OOOOOOOOOOC FD(M'S .............. 1.837615045698 1.837290064364 1.837290338603 Cpì(m) ............. 1.000036753652 1.000036747152 1.000036747157 Ctpl(m) ............ 0.986863807236 0.986864505954 0.986864505365 RhoGO(m)xCtpl(m) ... 602.579040698547 602.600017689212 602.599999985069 d e l t a Rho6O(m) ..... 0.020959301453 -0.000017689212 0.000000014931 . . E(M) ............... 0.021238291747 -0.000017924662 Dt(m) .............. 0.020091138288 0.020090044786 Dp(m j .............. .o . 000190615729 -0.000190569019 d e l t a Rho(m) ....... 0.020823885543 -0.000017574930 ~ho6O(m+l) ......... 610.620823885543 610.620806310613

output values Rho60 .......................... 610.620806310613 Ct1.o .......................... 0.986828242232 Fp. Ó ........................... 1.837290338603 c p l . o .......................... 1.000036747157 c t p l . o ......................... 0.986864505365 Ctpl .0. rounded ................ 0.98686

s tep 2 Correct ing 60' F

t corrected t o IP~

Rho60* ........... a l ha60 .......... C t l .............. Fp. p s i ........... P i n p s i .........

t. F ............ A ................ B ................

de?ta t. ......

CD1 ..............

and O .....

-5-68 ..... ..... ..... ..... ..... ..... ..... .....

p s i densi ty t o a l t e r n a t e condi t ......... -50.000000000000 'F ...... -50.016186329276 ......... 0.000006293511 ......... 1.563850526515 ......... 610.624649252968 ......... 0.000915424383 ......... -110.023061229276 ......... 1.097026730683 ......... 0.831793615513 ......... 0.000000000000 ......... 1.000000000000

c i p l ........................... 1.097026730683 Ctp l . rounded .................. 1.09703 Density a t t & P. kg/cu m ...... 669.867346834158

:ions:

s tep 3 volume a t base condi t ions ...... 495.107662 volume a t a l t e r n a t e t & P ...... 451.316428903



--`,,`,,,-`-`,,`,,`,`,,`---


commod; t y ...................... t observed temperature. ' F ..... 84.5

Speci a l i zed L i qu i d Alpha a t 6 0 ' ~ per ' F ........... 0.00057634

t a l t e r n a t e temperature. ' F .... 97.4 P observed pressure. PSI ....... 157 P a l t e r n a t e pressure. PSI ...... O Rho. observed dens i ty .......... 853.7 volume a t observed t & P ....... 10000


s tep 1

Correct ing observed dens i ty t o 60 ' F

~ho6O(m) . ~ho60* (m) C t l ( m ) ... d-al ha (m)

Cpl(m) ... Ctpl(m) . . Rho60 (m) xc

Fp(& ....

I t e r ...... ...... ...... .....

......

......

...... : tD1 (m)

-ation(m) . .... 853 . .... 853 . .... o . .... o . .... o . .... 1 . .... o . ... 842 .

O

703382614631 985817857839 000000000000 535641758165 O00841665365 986647586587 301044668997

~00000000000

d e l t a ' ~ h o 6 0 i m j .... 11.398955331003 E(M) ............... 11.553218683115

d e l t a Rho(m) ....... 11.579709574172

Dt(m) .............. 0.000000000000 Dp(m) .............. -0.002287699090

& O p s i reference condi t ions:

1 2 865.279709574172 865.279061018129 865.283138071074 865.282489512461

0.985817857839 0.985817857839 0.000000000000 0.000000000000 0.516633299257 0 . Si6634323827 1.000811772720 1.000811774331 0.986618117883 0.986618119472

853.700638502822 853.700000000034 -0.000638502822 -0.000000000034 -0.000647163082 0.000000000000

-0.002147788038 -0.000648556043

865.279061018129 RhoGO(m+lj .......... 865.279709574172 output ba i ues

Rho60 .......................... 865.279061018129

c p l . o .......................... 1.000811774331 c t p l . o ......................... 0.986618119472 Ctpl .0. rounded ................ 0.98662

C t l . o .......................... 0.985817857839 Fp. O ........................... 0.516634323827

. t. ' F .......................... t corrected t o IPTS-68 ' F ...... Rho60* ......................... a l ha60 ........................ C t l ............................ Fp. p s i ......................... P i n mi .......................

de?ta t. ....................

s tep 2 Correct inq 6 0 ' ~ and O p s i densi ty t o a l t e r n a t e condi t ions:

97.400000000000 97.416649907262

865.282489512461 0.000576340000

37.409775007262 0.978305995393 0.538697628351 0.000000000000

cp1 ............................ ctp1 ........................... c t p l . rounded .................. Density a t t & P. kg/cu m ......

volume a t base condi t ions ...... volume a t a l t e r n a t e t & P ......

s tep 3

1.000000000000 0.978305995393 0 . 97831

846.507693082447

9866.2 10084.9424007



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y . . . . . . . . . . . . . . . . . . . . . . t observed temperature, 'r . . . . . -57.9 t a l te rna te temperature, F .... 60 P observed pressure, PSI ....... 233 P a l te rna te pressure, PSI .. .... 245 Rho, observed A P I g rav i t y . . . . . . -14.1 volume a t observed t & P ....... 251.2

General i zed Lube O i 1



step 1


Note, Rho60 has been l i m i t e d t o the maximum tab le value i n one o r more cases.

KO(m) .......... K1(M) .......... K2(m) ..........

....

....

....

....

....

....

....

....

....

....

....

.... ...

....

....

....

....

....

....

Iterat ion(m) . . . . . O 1 2 ~ho6O(m) ........... 1.16350000000e+03 1.16281780211e+03 1.16281779744e+03

0.000000000000 0.000000000000 0.000000000000 0.348780000000 0.348780000000 0.348780000000 0.000000000000 0.000000000000 0.000000000000

A(m)- . . . . . . . . . . . B(M) ........... ~ho6O*(m) ...... al~ha60(m) . . . . . . . ct'i (m) . . . . . . . . . d-alpha(m) . . . . . cp l (m) . . . . . . . . . Fp(m) .......... c t p l (m) . . . . . . . . ~hoGO(m)xctpl (m) de l ta ~ho6O(m) . _ _ E(M) ........... Dt(m) .......... Dp(m) .......... de l ta Rho(m) . . . ~ho6O(m+l) .....

0.000002060874 0.000002062083 0.000002062083

1.000000000000 1.000000000000 1.000000000000 0.219692735298 0.219818332632 0.219818333493 i. 0005i21462 33 1.000512439174 1.000512439176 1.035477084142 1.035497647337 1.035497647478 1.20477758740e+03 1.20409509837e+03 1.20409509370e+03

-0.682493702536 -0.000004668362 -0.000000000031 -0.659110387848 -0.000004508327 -0.033344012152 -0.033362401069 -ö. ö00498813024 -Ö. ÖÖÖ499684129 -0.682197891836 -0.000004666339 1.16281780211e+03 1.16281779744e+03

output values Rho60 .......................... 1.16281779744e+03 Ct1,o .......................... 1.034967289693

cp1,o .......................... 1.000512439176 ctp1,o ......................... 1.035497647478 Ctpl,O, rounded ................ 1.03550

Fp,O ........................... 0.219818333493


........ 60.000000000000 F ...... 60.006874897736 ........ 0.000002062083 ........ 1.000000000000

t, 'F ................. A ..................... B ..................... t corrected t o IPTS-68

Rho60* ................ a l ha60 ............... de?ta t, .... ....... C t l .................... Fp,psi ................. P i n mi . . . . . . . . . . . . . . .

........ 1.16282019527e+03

........ 0.000299943191

........ -0.000000002264

........ 1.000000000001

........ 0.273551802459

........ 245.000000000000 cp l ............................ 1.000670651388 Ctpl ........................... 1.000670651389 Ctpl , rounded .................. 1.00067 Density a t t & P, kg/cu m ...... 1.16359764281e+03

step 3 volume a t base condit ions . . . . . . 260.1176 volume a t a l te rna te t & P ...... 259.943437897



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i 1 zed Lube O i t observed temperature. ' F ..... 302 t a l te rna te temperature. ' F .... 98.65 P observed pressure. PSI ....... 1499.97 P a l te rna te pressure. PSI ...... 568.33 Rho. observed A P I g rav i t y ...... 36.43 volume a t observed t & P ....... 999.6



step 1

Correcting observed density t o 60 ' F & O ps i reference condit ions:

I terat ion(m) ..... O 1 2 ~ho6O(m) ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) ......... ct?(m) ............. d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl (m) ... del t a ~ho6O(m) ..... Dt(m) .............. de l ta Rho(m) .......

Fp(& ..............

E(M) ............... Dp(m) .............. ~ho6O(m+l) .........

3 '841.783862323587 918.495586362405 917.505574875598 917.505498028854 .......... ~ .. ............

. 0 . oööööööööööo 0 . ooooooooooöö 0 . ööööooöoöööö 0.000000000000 0.348780000000 0.348780000000 0.348780000000 0.348780000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000002848507 0.000002610602 0.000002613419 0.000002613420 1.000000000000 1.000000000000 1.000000000000 1.000000000000

918.497984191115 0.000379728650 0.906037218501 1.000000000000 0.835056757732 1 . 0 12 68448 1602 0.917529830931

-0.044997474985

917.507972704310

0.917470106044 8 4 i . 783937077072

-0.000074753485 -0.000081477843 0.105533972802

-0.045269890050 76.711724038818 -0.990011486807 -0.000076846744

918.495586362405 917.505574875598 917.505498028854 output values

Rho60 .......................... 917.505498028854 C t l . o .......................... 0.905934133257 FP. o ........................... 0.838261567336 cp l . o .......................... 1.012733782436 c t p l . o ......................... 0.917470101411 Ctpl.0. rounded ................ 0.91747

step 2 Correctina 6 0 ' ~ and O mi densitv t o a l te rna te condit ions:

t. ' F .......................... A .............................. B .............................. t corrected t o IPTS-68 ' F ......

Rho60* ......................... alpha60 ........................ de l ta t. ' F .................... C t l ............................ Fp. ps i ......................... P i n ps i ....................... cp1 ............................ ctp1 ........................... c t p l . rounded .................. Density a t t & P . kg/cu m ......


step 3

0.98785 906.359235485755

917.103012 928.382863795

1.012733782436 0 . 917470101411

8 4 i . 783862321888 0.000000001699



--`,,`,,,-`-`,,`,,`,`,,`---



Commodity ...................... Generalized crude O i l t observed temperature, 'F ..... -58.05 t a l te rna te temperature, 'F .... -58.05 P observed pressure, PSI ....... -5 P a l te rna te pressure, PSI ...... -5

Forcing negative pressure(s1 t o zero Rho, observed A P I g r a v i t y ...... 169.16 volume a t observed t & P ....... 1000


Calcu lat ion o f Intermediate Results Density kg/cu meter ............ 470.168176677975 observed temperature less than -5O'C ( -58 '~ ) - outside l i m i t s o f t a b l e Al ternate temperature less than -5O'C ( -58 '~ ) - outside l i m i t s o f t a b l e Density less than 470.4 kg/cu m - outside l i m i t s o f tab le

Input Data Commodity ...................... Generalized crude O i l t observed temperature. 'F ..... 302.08 t a l te rna te temperature, 'F .... 302.06 P observed pressure, PSI ....... 1500.43 P a l te rna te pressure, PSI ...... O Rho, observed A P I g r a v i t y ...... -13.87 volume a t observed t & P ....... 1000


Calcu lat ion o f Intermediate Results Density kg/cu meter ............ 1201.740746408229 observed temperature greater than 150'C (302 '~) - outside l i m i t s o f tab le Al ternate temperature greater than 150.C (302 '~) - oufside l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o f tab le



--`,,`,,,-`-`,,`,,`,`,,`---


Example 1 2 Input Data

Commodity ...................... Generalized crude O i l t observed temperature. 'r ..... 89.08 t a l te rna te temperature. F .... 97.06 P observed pressure. PSI ....... 0.43 P a l te rna te pressure. PSI ...... 27.75 Rho. observed API g rav i t y ...... -9.1 volume a t observed t & P ....... 1000



step 1


I terat ion(m) ..... 0 1 2 ~ho6O(m) ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) ......... ct?(m) ............. d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl (m) ... del t a ~ho6O(m) ..... Dt(m) ..............

Fp(& ..............

E(M) ...............

. . 1.15490820261e+03 1.16345254536e+03 1.16345298090e+03

341.095700000000 341.095700000000 341.095700000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000001758116 0.000001732388 0.000001732387 2.000000000000 2.000000000000 2.000000000000

Dpimj .............. de l ta Rho(m) ....... ~ho6O(m+l) ......... Rho60 .........................

output values

1 . O . O . 2 . O . 1 . O . 1 . 8 . 8 . O .

-0 .

15491023307e 000255728885 992545110373 000000000000 2916663737 54 000001254167 992546355190 ...........

14629992708e 608275530558 672920398676 015050161444

+03

+O3

1.000001240466 1.000001240466 0.992655668224 0.992655673734 ¡.1549¿¡776386e+03 ¡.1549¿¡820262e+03 0.000438752057 -0.000000001698 0.000441998239 0 . 014827366651 . 0.000001834864 000001882680

8.544342747166 0.000435541110 1.16345254536e+03 1.16345298090e+03

C t l . o .......................... cp1. o .......................... ctp1. o ......................... Fp. O ...........................

c tp l .0 . rounded ................ step 2

Correctina 60'F and O mi densi t v t. 'F .......................... A .............................. B .............................. t corrected t o IPTS-68 'F ......

Rho60* ......................... alpha60 ........................ de l ta t. 'F .................... C t l ............................ Fp. ps i ......................... P i n ps i ....................... cp1 ............................ ctp1 ........................... c t p l . rounded .................. Density a t t & P. kg/cu m ......


step 3

1.16345298090e+03 0 . 992654442380 0.288480047418 1.000001240466 0.992655673734 0 . 99266

t o a l te rna te condit ions: . 97.060000000000

0.000251986379

0 . 99071 1.15264886504e+03

992.66 1001.96828537



--`,,`,,,-`-`,,`,,`,`,,`---


Example 1 3 Inpu t Data

Commodity ...................... Generalized Crude O i l t observed temperature. 'F ..... 87.9 t a l ternate temperature. 'F .... 237.8 P observed pressure. P S I ....... 172.34 P a l ternate pressure. PSI ...... O Rho. observed A P I g rav i t y ...... 105.3 volume a t observed t & P ....... 1000


Calculat ion o f Intermediate Results Density kg/cu meter ............ 596.962685810811

step 1

Correct ing observed densi ty t o 60 'F & O ps i reference condi t ions:

Note. Rho60 has been l i m i t e d t o the minimum tab le value i n one o r more cases

I terat ion(m) ..... 0 1 Rho6O(m) ........... 610.600000000000 610.603878491534

Kï(m) .............. 0.000000000000 0.000000000000 K2(m) .............. 0.000000000000 0.000000000000 A(m) ............... 0.000006289685 0.000006289605 B(m) ............... 2.000000000000 2.000000000000 Rho6O*(m) .......... 610.603840464675 610.607718931815 a l ha60(m) ......... 0.000914865355 0.000914853733

d-alpha(m) ......... 2.000000000000 2.000000000000 Fp(m) .............. 2.003652617491 2.003584457334 Cpl(m) ............. 1.003465060102 1.003464941820 Ctpl(m) ............ 0.977659290629 0.977659505442 RhoGO(m)xCtpl(m) ... 596.958762857874 596.962685866784 de l ta ~ho6O(m) 0.003922952936 -0.000000055974 E(m) ............... 0.004012597204 Dt(m) .............. 0.053134326876

de l ta Rho(m) ....... 0.003878491534 RhoGO(m+l) ......... 610.603878491534

KO(m) .............. 341.095700000000 341.095700000000

Ct?(m) ............. 0 . 974283340298 0.974283669212

.....

Dp(m) .............. -0.018557567083

output values Rho60 .......................... 610.603878491534 C t l . o .......................... 0.974283669212

Cpl. o .......................... 1.003464941820 Ctp l . o ......................... 0.977659505442

Fp. O ........................... 2.003584457334

Ctpl.0. rounded ................ 0.97766

step 2 Correct ing 6 0 ' ~ and O ps i densi ty t o a l ternate condi t ions:

t. F .......................... 237.800000000000 t corrected t o IPTS-68 'F ...... 237.851832056034 A .............................. 0.000006289605 B .............................. 2.000000000000 Rho60* ......................... 610.607718931815 a l ha60 ........................ 0.000914853733 de?ta t . O F .................... 177.844957156034 C t l ............................ 0.832034523163 Fp. ps i ......................... 5.209412010592 P i n ps i ....................... 0.000000000000 cp1 ............................ 1.000000000000 Ctpl ........................... 0.832034523163 Ctp l . rounded .................. 0.83203 Density a t t & P. kg/cu m ...... 508.043506882197

volume a t base condi t ions ...... 977.66 volume a t a l ternate t & P ...... 1175.02974652

step 3



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i zed Refined product t observed temperature, ' F ..... -58.05 t a l te rna te temperature, ' F .... -58.05 P observed pressure, PSI ....... O P a l te rna te pressure, PSI ...... O Rho, observed densi ty .......... 470.17 volume a t observed t & P ....... 1000

observed temperature less than -5O'C (-58'~) - outside l i m i t s o f t a b l e Al ternate temperature less than -5O'C (-58'~) - outside l i m i t s o f t a b l e Density less than 470.3 kg/cu m - outside l i m i t s o f tab le


Example 1 5 Input Data

Commodi t y ...................... General i zed Refined product t observed temperature, ' F ..... 302.08 t a l te rna te temperature, ' F .... 302.05 P observed pressure, PSI ....... 1500.5 P a l te rna te pressure, PSI ...... O Rho, observed densi ty .......... 1209.56 volume a t observed t & P ....... 1000

observed temperature greater than 150'C (302'~) - outside l i m i t s o f tab le Al ternate temperature greater than 150'C (302'~) - outside l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1209.5 kg/cu m - outside l i m i t s o f t a b l e




--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i zed Lube O i 1 t observed temperature, ' F ..... -58.05 t a l te rna te temperature, ' F .... -58.05 P observed pressure, PSI ....... O P a l te rna te pressure, PSI ...... O Rho, observed A P I g r a v i t y ...... -10.05 volume a t observed t & P ....... 1000


Calcu lat ion o f Intermediate Results Density kg/cu meter ............ 1163.942066694113 observed temperature less than -5O'C (-58'~) - outside l i m i t s o f t a b l e Al ternate temperature less than -5O'C (-58'~) - outside l i m i t s o f t a b l e


Commodi t y ...................... General i zed Lube O i 1 t observed temperature, ' F ..... 302.05 t a l te rna te temperature, ' F .... 302.05 P observed pressure, PSI ....... 1500.5 P a l te rna te pressure, PSI ...... O Rho, observed A P I g r a v i t y ...... 45 .O8 volume a t observed t & P ....... 1000


Calcu lat ion o f Intermediate Results Density kg/cu meter ............ 800.547989579794 observed temperature greater than 150'C (302'~) - outside l i m i t s o f tab le Al ternate temperature greater than 150.C (302'~) - oufside l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o f tab le



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y . . . . . . . . . . . . . . . . . . . . . . t observed temperature, 'r ..... -57.95 t a l te rna te temperature, F .... 60 P observed pressure, PSI ....... 233.7 P a l te rna te pressure, PSI .. .... 245.66 Rho, observed A P I g rav i t y ...... -14.15 volume a t observed t & P . . . . . . . 1000

General i zed Lube O i 1



step 1


Note, Rho60 has been l i m i t e d t o the maximum tab le value i n one o r more cases.

KO(m) .......... K1(M) .......... K2(m) ..........

....

....

....

....

....

....

....

....

....

....

....

.... ...

....

....

....

....

....

....

Iterat ion(m) . . . . . O 1 2 ~ho6O(m) ........... 1.16350000000e+03 1.16331178872e+03 1.16331178744e+03

0.000000000000 0.000000000000 0.000000000000 0.348780000000 0.348780000000 0.348780000000 0.000000000000 0.000000000000 0.000000000000

A(m)- . . . . . . . . . . . B(M) ........... ~ho6O*(m) ...... al~ha60(m) . . . . . . . ct'i (m) . . . . . . . . . d-alpha(m) . . . . . cp l (m) . . . . . . . . . Fp(m) .......... c t p l (m) . . . . . . . . ~hoGO(m)xctpl (m) de l ta ~ho6O(m) . _ _ E(M) ........... Dt(m) .......... Dp(m) .......... de l ta Rho(m) . . . ~ho6O(m+l) .....

0.000002060874 0.000002061207 0.000002061207

1.000000000000 1.000000000000 1.000000000000 0.219672384586 O . 219706997026 O . 219706997262 i. 000513638051 i. 0005i37i9ö24 i. 0005i37i9024 1.035493272457 1.035498945759 1.035498945797 1.20479642250e+03 1.20460813081e+03 1.20460812953e+03

-0.188292976336 -0.000001282839 -0.000000000009 -0.181838918074 -0.000001238861 -0.033357305031 -0.033362378201 .~ .____ ~ _._._ ~ .~ .___.

-0.000500177750 -0.000500418486 -0.188211278184 -0.000001282283 1.16331178872e+03 1.16331178744e+03

output values Rho60 .......................... 1.16331178744e+03 Ct1,o .......................... 1.034967263424

cp1,o .......................... 1.000513719024 Fp,O ........................... 0.219706997262

C t D l . 0 ......................... 1.035498945797 Ctpl ; O , rounded . . . . . . . . . . . . . . . . 1.03550


........ 60.000000000000 F ...... 60.006874897736 ........ 0.000002061207 ........ 1.000000000000

t, 'F ................. A ..................... B ..................... t corrected t o IPTS-68

Rho60* ................ a l ha60 ............... de?ta t, .... ....... C t l .................... Fp,psi ................. P i n mi . . . . . . . . . . . . . . .

........ 1.16331418527e+03

........ 0.000299815823

........ -0.000000002264

........ 1.000000000001

........ 0.273391493229

........ 245.660000000000 cp l ............................ 1.000672064910 Ctpl ........................... 1.000672064911 Ctpl , rounded .................. 1.00067 Density a t t & P, kg/cu m ...... 1.16409360847e+03

step 3 volume a t base condit ions . . . . . . 1035.5 volume a t a l te rna te t & P ...... 1034.8066795



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.7 Implementation Procedures for Metric Units (15°C or 20°C and O kPa Base Conditions)

11.1.7.1 Method to Correct a Measured Volume to Metric Base Conditions and Density from Metric Base Conditions to an Alternate Temperature and Pressure


This procedure calculates the Volume Correction Factor (VCF) given the density at the metric base conditions (1 5°C or 20°C and O kPa (gauge)). The parameters used in this procedure depend upon the commodity group to which the liquid belongs. Because the VCF expressions were developed and expressed in terms of a base density at 60°F, this calculation must be done as a two part process:

1.

2.

Calculate the density at 60°F and O psig consistent with the metric base density.

Calculate the density at the alternate metric temperature and pressure conditions.

The procedure has been written assuming that the input values are all in the proper units (“Cy kPa or bar (gauge), and kg/m3). If they are not in the proper units then apply the procedures in 11.1.5.1. The density values calculated by this procedure are in kg/m3.

Input Values


a60 Pre-calculated 60°F thermal expansion factor (if commodity group not given)

p T Density at metric base conditions (1 5°C or 20°C and O kPa (gauge)) (kg/m3)

T Base temperature (1 5°C or 20°C)

t Alternate temperature (“C)

P Alternate pressure (kPa or bar (gauge))


Volume at alternate conditions (t and P) (any valid set of units, such as liters, cubic metres, and barrels)

Output Values

CTL Volume correction factor due to temperature

CpL Volume correction factor due to pressure

Fp Scaled compressibility factor (kPa-’ or bar-’)

CTpL Combined volume correction factor due to temperature and pressure


P Density at alternate conditions (kg/m3)

VT Volume at base conditions (same set of units as Y,)



--`,,`,,,-`-`,,`,,`,`,,`---


p60 Density at 60°F and O psig (kg/m3)

Intermediate Values

K F Base temperature T converted to units of OF (OF)

tOF Alternate temperature t converted to units of OF (OF)

Ppd Alternate pressure P converted to units of psig @Sig)

CTL,60 CTL value correcting &O to p T

C;L CTL value correcting p60 to the alternate temperature

C;pL CTPL value correcting p60 to the alternate temperature and pressure

Fp,psi Scaled compressibility factor (psi-')


Step 1: Convert the base temperature, alternate temperature, and alternate pressure into customary units using equations in 1 1.1.5.1. Call these variables E , , toF , and Ppsi .

Step 2: Calculate the correction factors for the density at 60°F, p60 , corresponding to the metric base density p T value at E , using the procedure in 11.1.6.2. The pressure correction need not be calculated since the metric base pressure (O Wa (gauge)) is the same as the base pressure in 1 1.1.6.1 (O psig). If this procedure returns with an error condition (i.e. fluid outside the limits of this Standard), exit this procedure. Call the CTL associated with this step CTL.60 .

Step 3: Using this value of p60 , calculate the density value at the alternate conditions to, and Ppsi using the procedure in 11.1.6.1. There are associated factors that must be adjusted to take into account that the reference temperature is not 60°F and the originally input pressure is not in customary units. Call these factors C;L , CpL , C;pL , and Fp,psi .

Step 4: Calculate the correction factors for the metric base temperature by combining the correction factors for 60°F. The temperature correction factor is:

G L c,, =- 'TL,60

and the combined temperature and pressure correction factor is:

c,, = c, . CPL .


Modi9 the scaled compressibility factor for the metric pressure units:

for Wa F',psi F - - 6.894757

F - F',psi for bar * - 0.06894757



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Step 5: Optionally, correct a volume measured at alternate condtions to base conditions andíor correct base density to alternate conditions.:

P = C T L a c m ~ P T

V T = V , , p * C T p L




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API MPMS 11.1.7.1 Metr ic un i t s . Example 1 A volume o f a crude o i l i s measured a t observed condit ions o f temperature and pressure . The base density a t 1 5 ' C i s known . Calculate the volume a t base condit ions and cor rec t the base density t o an a l te rna te condi t i on .

Commodity ...................... Generalized crude O i l Inpu t Data

T base temperature. 'C ......... 1 5 t a l te rna te temperature. 'C .... -32.8 P a l ternate pressure. bar ...... 24.6 Base densi t kg/cu m .......... 772.3 volume a t oke rved t & P .......

t a l te rna te temperature, ' F .... -27.04

9885


step 1 . convert t o customary u n i t s

T base. F ..................... 59 P alternate. P S I ............... 356.792849987

step 2 . correc t base metr ic (observed) density t o 60 ' F & O ps i reference condit ions:

I terat ion(m) ..... 0 Rho60(m) ........... 772.300000000000 KO(m) .............. 341.095700000000 Kï(m) .............. 0.000000000000 Kï(m) .............. 0.000000000000

............... 0.000003931610

d-al pha(m) ......... 2.000000000000 Rho60ím)xCt1.60ím) . 772.741697581079 . . delta'Rho6Ö(m) ...... -0.441697581079 E(M) ............... -0.441445107641 Dt(m) .............. -0.001142702545

2.000000000000 772 3ööööö27Söii -0.000000275011

Dp(m) .............. -0.000000000000 del t a Rho(m) ....... -0.441950125174 Rho60(m+l) ......... 771.858049874826

Rho60 .......................... 771.858049874826 C t l , 60 ......................... 1.000572579894

step 3 . correc t 6 0 ' ~ / 0 ps i density t o a l te rna te condit ions: t, ' F .......................... -27.040000000000 t corrected t o IPTS-68 ' F ...... -27.052381115706 A .............................. 0.000003936113 B .............................. 2.000000000000 Rho60* ......................... 771.861087987332 a l ha60 ........................ 0.000572529607 de?ta t , O F .................... -87.059256015706 C t l * ........................... 1.049020399586 Fp, ps i ......................... 0.462386457487 P i n ps i ....................... 356.792849987316 cp l ............................ 1.001652488031 Ctpl* .......................... 1.050753893241

C t l ............................ 1.048420095319 Ctpl ........................... 1.050152596978

Fp, bar ......................... 6.706348860257

volume a t base condit ions ...... 10380.73275 Density, kg/cu m , a t t & P ..... 811.030845

step 4 . Modify C t l and Ctpl for temperature base o f 15'c

Ctpl , rounded .................. 1.05015

step 5 . calcu la te volume a t base condit ions and density a t a l te rna te condit ions



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API MPMS 11.1.7.1 Metr ic un i t s . Example 2 A volume o f a crude o i l i s measured a t observed condit ions o f temperature and pressure . a t 20': i s known . condi t i on .

Input Data Commodity ...................... Generalized crude O i l

The base density ca lcu la te the volume a t base condit ions and cor rec t the base density t o an a l te rna te

T base temperature. 'c ......... 20 t a l te rna te temperature. 'c .... -32.8 P a l ternate pressure. bar ...... 24.65 Base density. kg/cu m .......... 772.3 volume a t observed t & P ....... 397498


step 1 - convert t o cystomary u n i t s t a l te rna te temperature. F .... -27.04 T base. F ..................... 68 P al ternate. PSI ............... 357.518038707

step 2 . correc t base metr ic (observed) density t o 60 ' F & O ps i reference condit ions:

I terat ion(m) ..... 0 1 2 ~ho6O(m) ........... 772.300000000000 775.822822685260 775.822887700255 KO(m) .............. 341.095700000000 341.095700000000 341.095700000000

0.000000000000 0.000000000000 0.000000000000 K i i m j .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) .........

~hoGO(m)xctl. 60(m) . del t a ~ho6O(m) ..... Dt(m) .............. de l ta Rho(m) .......

C t ? . 6O(m) .......... d-al pha(m) .........

E(M) ............... Dp(m) .............. ~hoGO(m+l) .........

0.000000000000 0 . 000003931610 2.000000000000

772.303036373950 0.000571874537 0.995417583056 2.000000000000

768.760999394329 3.539000605671 3.555292437978 0.009216970486

-0.000000000000

0.000000000000 ö: ö00003895986 2.000000000000

775.825845271850 0.000566692882 0.995459159111 2.000000000000

3.522822685260 0.000065014995 775.822822685260 775.822887700255

Rho60 .......................... 775.822887700255 C t l . 60 ......................... 0.995459159873

step 3 . correc t 6 0 ' ~ / 0 ps i

t corrected t o IPTS-68 ' F ...... t. ' F .......................... A .............................. B .............................. Rho60* ......................... a l ha60 ........................ C t l * ........................... Fp. ps i ......................... P i n ps i .......................

de?ta t. ....................

CD1 ............................

density t o a l terna -27.040000000000 -27.052381115706

0.000003895985 2.000000000000

775.825910286592 0.000566692787 0.000566692787

1.048529743821 0.456638589390

357.518038706803 1.001635234957

-87.059256015706

1.001635234957

0.000000000000

2.000000000000 772 : 3ööööööööiSS -0.000000000155

t e condi t i ons :

c i p l * .......................... 1.050244336311

step 4 . Modify C t l and Ctpl f o r temperature base o f 20'C C t l ............................ 1.053312668251 C t D 1 ........................... 1.055035081947 Ctpl . rounded .................. 1.05504 Fp. bar ......................... 6.622983078151

volume a t base condit ions ...... 419376.28992 Density. kg/cu m . a t t & P ..... 814.807392




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API MPMS 11.1.7.1 Metr ic un i t s . Example 3 A volume o f a re f ined product i s measured a t observed condit ions o f temperature and pressure . The base density a t 1 5 ' C i s known . ca lcu la te the volume a t base condit ions and correct the base density t o an a l te rna te condi t ion .

Commodi t y ...................... General i zed Refined product Input Data

T base temperature. 'c ......... 1 5 t a l te rna te temperature. 'c .... 87.32 P a l te rna te pressure. kpa ...... 75 Base density. kg/cu m .......... 865.6 volume a t observed t & P ....... 48.75


step 1 - convert t o cystomary u n i t s t a l te rna te temperature. F .... 189.176 T base. F ..................... 59 P al ternate. PSI ............... 10.8778307923

step 2 - cor rec t base metr ic (observed) density t o 60 'F & O ps i reference condit ions:

I terat ion(m) ..... O Commodity .......... fue l o i l ~ho6O(m) ........... 865.600000000000 KO(m) .............. 103.872000000000

1 f ue l o i l

865.209800869528 103.872000000000

2 f ue l o i l

865.209799447010 103.872000000000

K i i m j .............. o . 27oioooooooo K2(m) .............. 0.000000000000 A(m) ............... 0.000003098311 B(M) ............... 1.307613432453 ~ho6O*(m) .......... 865.602681897543 a l ~ha6O(m) ......... O . 000450668230 c t i .60( i i. .......... 1.000450723728 d-alpha(m) ......... 1.300000000000 ~ho60(m)xctl . 60(m) . 865.990146458899 de l ta ~hoGO(m1 ..... -0.390146458899 . . E(M) ............... -0.389970689856 Dt(m) .............. -0.000585446247

0.2 70100000000 0.000000000000 0.000003100138 1.307709473868

865.212483139130 0.000450934024 1.000450989520 1.300000000000

865.600001422325 -0.000001422325 -0.000001421684 -0.000585791280

0.2 70100000000 0.000000000000 0.000003100138 1.307709474219

865.212481716614 0.000450934025 1.000450989521 1.300000000000

865.600000000005 -0.000000000005

opimj .............. .o . oooooooooooo -0.000000000000 de l ta Rho(m) ....... -0.390199130472 -0.000001422518 RhoGO(m+l) ......... 865.209800869528 865.209799447010

Rho60 .......................... 865.209799447010 C t l . 60 ......................... 1.000450989521

step 3 . correc t 6 0 ' ~ / 0 ps i density t o a l te rna te condit ions: t. 'F .......................... ~89.176000000000 t corrected t o IPTS-68 'F ...... 189.216725285673 A .............................. 0.000003100138 B .............................. 1.307709474219 Rho60* ......................... 865.212481716614 a l ha60 ........................ 0.000450934025 de?ta t . O F .................... 129.209850385673 C t l * ........................... 0.940840865293 Fp. ps i ......................... 0.725556454792 P i n Dsi ....................... 10.877830792296 cp l ............................ 1.000078931033 Ctpl* .......................... 0.940915126834

step 4 . Modify C t l and Ctpl f o r temperature base o f 1 5 ' C C t l ............................ 0.940416747194 Ctpl ........................... 0.940490975260 Ctpl , rounded .................. 0.94049 Fp. kPa ......................... 0.105233071273





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API MPMS 11.1.7.1 Metr ic un i t s . Example 4 A volume o f a re f ined product i s measured a t observed condit ions o f temperature and pressure . The base density a t 1 5 ' C i s known . ca lcu la te the volume a t base condit ions and correct the base density t o an a l te rna te condi t ion .

Commodi t y ...................... General i zed Refined product T base temperature. 'c ......... 1 5 t a l te rna te temperature. 'c .... 27.37 P a l ternate pressure. bar ...... 17.05 Base density. kg/cu m .......... 793.5 volume a t observed t & P ....... 200.2

Input Data


step 1 - convert t o cystomary u n i t s t a l te rna te temperature. F .... 81.266 T base. F ..................... 59 P al ternate. PSI ............... 247.289353345


I terat ion(m) ..... 0 1 Commodity .......... j e t fue l j e t fue l ~ho6O(m) ........... 793.500000000000 793.083483971112 KO(m) .............. 330.301000000000 330.301000000000 K i i m j .............. 0 . oooooooooooo 0.000000000000 K2(m) .............. 0.000000000000 0.000000000000 A(m) ............... 0.000003606470 0.000003610259 B(M) ............... 2.000000000000 2.000000000000 ~hoGO*(m) .......... 793.502861726357 793.086347200399 al~ha60(m) ......... 0.000524581407 0.000525132553 c t i .60( i i. .......... 1.000524634773 1.000525185891 d-alpha(m) ......... 2.000000000000 2.000000000000 ~ho60(m)xctl . 60(m) . 793.916297692263 793.500000227253 de l ta ~hoGO(m1 ..... -0.416297692263 -0.000000227253 . . E(M) ............... -0.416079402540 Dt(m) .............. -0.001048282220 Dpimj .............. .o . oooooooooooo de l ta Rho(m) ....... -0.416516028888 ~hoGO(m+l) ......... 793.083483971112

Rho60 .......................... 793.083483971112 C t l . 60 ......................... 1.000525185891

step 3 . correc t 6 0 ' ~ / 0 ps i density t o a l te rna te condit ions: t. 'F .......................... 8~.266000000000 t corrected t o IPTS-68 'F ...... 81.278374938351 A .............................. 0.000003610259 B .............................. 2.000000000000 Rho60* ......................... 793.086347200399 a l ha60 ........................ 0.000525132553 de?ta t . O F .................... 21.271500038351 C t l * ........................... 0.988793028121 Fp. ps i ......................... 0.656392797417 P i n Dsi ....................... 247.289353344868 cp l ............................ 1.001625828532 Ctpl* .......................... 0.990400636038

step 4 . Modify C t l and Ctpl f o r temperature base o f 1 5 ' C C t l ............................ 0.988274000560 Ctpl ........................... 0.989880764627 c t p l , rounded .................. 0.98988 Fp. bar ......................... 9.520173044783

vo l Ume a t base condi t i ons ...... 198.173976 Density. kg/cu m . a t t & P ..... 785.46978




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API MPMS 11.1.7.1 Metr ic un i t s . Example 5 A volume o f a re f ined product i s measured a t observed condit ions o f temperature and pressure . The base density a t 20'C i s known . ca lcu la te the volume a t base condit ions and correct the base density t o an a l te rna te condi t ion .


T base temperature. 'c ......... 20 t a l te rna te temperature. 'c .... -36 P a l ternate pressure. bar ...... 8.6 Base density. kg/cu m .......... 772.3 volume a t observed t & P ....... 1502.3


step 1 - convert t o cystomary u n i t s t a l te rna te temperature. F .... -32.8 T base. F ..................... 68 P al ternate. PSI ............... 124.732459752


I terat ion(m) ..... O 1 2 3 Commodity .......... t rans i t i on t rans i t i on t rans i t i on t rans i t i on ~ho6O(m) ........... 772.300000000000 776.046081952777 776.056443403059 776.056458538058 KO(m) .............. 1.48906700000e+03 1.48906700000e+03 1.48906700000e+03 1.48906700000e+03 K i i m j .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l pha60(m) .........

~hoGO(m)xctl. 60(m) . del t a ~ho6O(m) ..... Dt(m) ..............

C t l . 60(m) .......... d-al pha(m) .........

E(M) ...............

0.000000000000 -0.001868400000 0.000004318542 7.948794061670

772.303335114335 0.000628139366 0.994966066092 8.500000000000

768.412292842796 3.887707157204 3.907376632928 0.043056901100

0.000000000000 -0.001868400000 0.000004153240 8.185560760776

776.049304966171 0.000604096073 0.995159024472 8.500000000000

772.289261861302 0.010738138698 0 . 010790374638 0.041396169845

0.000000000000 -0.001868400000 0.000004152786 8.186236842691

776.059666107245 0.000604030053 0.995159554282 8.500000000000

772.299984314832 0.000015685168 0.000015761461 0.041391611065

0.000000000000 -0.001868400000 0.000004152785 8.186237830334

776.059681241792 0.000604029957 0.995159555056 8.500000000000

772.299999977145 0.000000022855

_ _ DD(m) .............. -0.000000000000 -0.000000000000 -0.000000000000 ............

déì tá Rho(m) ....... 3.746081952777 0. 010361450282 0. 000015134999 ~hoGO(m+l) ......... 776.046081952777 776.056443403059 776.056458538058

Rho60 .......................... 776.056458538058 C t l . 60 ......................... 0.995159555056

step 3 . correc t 6 0 ' ~ / 0 ps i density t o a l te rna te condit ions: t. 'F .......................... -32.800000000000 t corrected t o IPTS-68 'F ...... -32.813394933532 A .............................. 0.000004152785 B .............................. 8.186237830334 Rho60* ......................... 776.059681241792 a l ha60 ........................ 0.000604029957 de?ta t . O F .................... -92.820269833532 C t l * ........................... 1.055011702151 Fp. ps i ......................... 0.445919193636 P i n mi ....................... 124.732459751663 cp l ............................ 1.000556515516 Ctpl* .......................... 1.055598832533

step 4 . Modify C t l and Ctpl f o r temperature base o f 20'C C t l ............................ 1.060143267269 Ctpl ........................... 1.060733253446 Ctpl , rounded .................. 1.06073 Fp. bar ......................... 6.467511380549





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A P I MPMS 11.1.7.1 Metr ic Uni ts. Example 6 A volume o f a re f ined product i s measured a t observed condit ions o f temperature and pressure . The base density a t 1 5 ' C i s known . ca lcu la te the volume a t base condit ions and correct the base density t o an a l te rna te condi t ion .


T base temperature. 'c ......... 1 5 t a l te rna te temperature. 'c .... 27.35 P a l te rna te pressure. kpa ...... 1235 Base density. kg/cu m .......... 657.3 volume a t observed t & P ....... 1000


step 1 - convert t o cystomary u n i t s t a l te rna te temperature. F .... 81.23 T base. F ..................... 59 P a l ternate. PSI ............... 179.121613713


I terat ion(m) ..... O 1 2 Commodity .......... gasoline gasoline gasoline ~ho6O(m) ........... 657.300000000000 656.763177196090 656.763156816252 KO(m) .............. 192.457100000000 192.457100000000 192.457100000000 K i i m j .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l pha60(m) .........

~hoGO(m)xctl. 60(m) . del t a ~ho6O(m) ..... Dt(m) ..............

C t l . 60(m) .......... d-al pha(m) .........

E(M) ...............

0.243800000000 0.000000000000 O . 000005612455 1.545657407721

657.303689061482 0.000816362130 1.000816376104 1.500000000000

657.836604013187 -0.536604013187 -0.536166299832 -0.001222943721

0.243800000000 0.000000000000 0.000005619548 1.545859957612

656.766867902911 0.000817393796 1.000817407544 1.500000000000

657.300020371521 -0.000020371521 -0.000020354883 -0.001224487176

0.243800000000 0.000000000000 0.000005619548 1.545859965304

656.766847523136 0.000817393835 1.000817407583 1.500000000000

657.300000000770 -0.000000000770

opimj .............. .o . oooooooooooo -0.000000000000 de l ta Rho(m) ....... -0.536822803910 -0.000020379838 RhoGO(m+l) ......... 656.763177196090 656.763156816252

Rho60 .......................... 656.763156816252 C t l . 60 ......................... 1.000817407583

step 3 . correc t 6 0 ' ~ / 0 ps i density t o a l te rna te condit ions: t. 'F .......................... 8~.230000000000 t corrected t o IPTS-68 'F ...... 81.242365479576 A .............................. 0.000005619548 B .............................. 1.545859965304 Rho60* ......................... 656.766847523136 a l ha60 ........................ 0.000817393835 de?ta t . O F .................... 21.235490579576 C t l * ........................... 0.982555008412 Fp. ps i ......................... 1.342969568596 P i n mi ....................... 179.121613713145 cp l ............................ 1.002411349381 Ctpl* .......................... 0.984924291823

step 4 . Modify C t l and Ctpl f o r temperature base o f 1 5 ' C C t l ............................ 0.981752516460 Ctpl ........................... 0.984119864783 Ctpl , rounded .................. 0.98412 Fp. kPa ......................... 0.194781276352

vo l Ume a t base condi t i ons ...... 984.12 Density. kg/cu m . a t t & P ..... 646.862076




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API MPMS 11.1.7.1 Metr ic un i t s . Example 7 A volume o f a special ized l i q u i d i s measured a t observed condit ions o f temperature and pressure . The base density a t 1 5 ' C i s known . ca lcu la te the volume a t base condit ions and correct the base density t o an a l ternate condi t i on .

Commodi t y ...................... Speci a l i zed L i qui d Alpha a t 6 0 ' ~ per ' F ........... 0.000446759

Input Data

T base temperature, 'c ......... 1 5 t a l te rna te temperature. 'c .... 89.9 P a l ternate pressure. bar ...... 45.35 Base densi t kg/cu m .......... 641.8 volume a t oke rved t & P .......

t a l te rna te temperature, F .... 193.82

47.85


step 1 - convert t o cystomary u n i t s

T base. F ..................... 59 P al ternate. PSI ............... 657.746168574

step 2 - cor rec t base metr ic (observed) density t o 60 ' F & O ps i reference condit ions:

I terat ion(m) ..... 0 1 ~ho6O(m) ........... 641.800000000000 641.513362513010 ~ho6O*(mì .......... 641.801971246791 641.515332879412 c t l . 6o(mj .......... 1.000446814523 1.000446814523 d-alpha(m) ......... 0.000000000000 0.000000000000 ~ho60(m)xctl . 60(m) . 642.086765560782 641.800000000000 de l ta ~ho6O(m) ..... -0.286765560782 -0.000000000000 E(M) ............... -0.286637486990 Dt(m) .............. -0.000000000000 Dpimj .............. .o . oooooooooooo de l ta Rho(m) ....... -0.286637486990 ~hoGO(m+l) ......... 641.513362513010

Rho60 .......................... 641.513362513010 C t l . 60 ......................... 1.000446814523

step 3 . correc t 6 0 ' ~ / 0 ps i density t o a l te rna te condit ions: t. ' F .......................... 193.820000000000 t corrected t o IPTS-68 ' F ...... 193.861860191643 Rho60* ......................... 641.515332879412 a l ~ h a 6 0 ........................ 0.000446759000 dei t a t . . F .................... 133.854985291643 C t l * ........................... 0.939260765097 Fp. ps i ......................... 2.875296454594 P i n ps i ....................... 657.746168574179 CD1 ............................ 1.019276716462 C ip l * .......................... 0.957366628549

step 4 . Modify C t l and Ctpl f o r temperature base o f 1 5 ' C C t l ............................ 0.938841277179 C t D 1 ........................... 0.956939054283 Ctpl . rounded .................. 0.95694 Fp. bar ......................... 41.702651081010





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API MPMS 11.1.7.1 Met r ic u n i t s , Example 8 A volume o f a crude o i l i s measured a t observed condi t ions o f temperature and pressure. The base densi ty a t 1 5 ' C i s known. c a l c u l a t e the volume a t base condi t ions and c o r r e c t the base dens i ty t o an a l t e r n a t e condi t i on.

Commodity ...................... Generalized crude O i l I n p u t Data

T base temperature, 'c ......... 15 t a l t e r n a t e temperature, 'c .... -50.025 P a l t e r n a t e pressure, kpa ...... - 5

Base dens i t kg/cu m .......... 610.46 Forcing negative pressure t o zero

volume a t o k e r v e d t & P .......

t a l t e r n a t e temperature, F .... -58.045

1000


s tep 1 - convert t o cystomary u n i t s

T base, F ..................... 59 P a l te rna te , PSI ............... O A l te rna te temperature l e s s than -5O'C ( - 5 8 ' ~ ) - outs ide l i m i t s Density l e s s than 610.6 kg/cu m - outs ide l i m i t s o f t a b l e

o f tab1 e

API MPMS 11.1.7.1 Met r ic u n i t s , Example 9 A volume o f a r e f i n e d product i s measured a t observed condi t ions o f temperature and pressure. The base densi ty a t 20'C i s known. c a l c u l a t e the volume a t base condi t ions and cor rec t the base dens i ty t o an a l t e r n a t e condi t ion.

Commodi t y ...................... General i zed Refined product I n p u t Data

T base temperature, 'c ......... 20 t a l t e r n a t e temperature, 'c .... 150.025 P a l t e r n a t e pressure, kpa ...... 10343 Base densi ty , kg/cu m .......... 1163.55 volume a t observed t & P ....... 1000


s tep 1 - convert t o cystomary u n i t s t a l t e r n a t e temperature, F .... 302.045 T base, F ..................... 68 P a l te rna te , PSI ............... 1500.12538513 A l te rna te temperature greater than 150'C ( 3 0 2 ' ~ ) - outs ide l i m i t s o f t a b l e A l te rna te pressure greater than 1500 p s i - outs ide l i m i t s o f t a b l e Density greater than 1163.5 kg/cu m - outs ide l i m i t s o f t a b l e



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API MPMS 11.1.7.1 Metr ic u n i t s , Example 10 A volume o f a lube o i l i s measured a t observed condit ions o f temperature and pressure. The base density a t 15': i s known. ca lcu la te the volume a t base condit ions and cor rec t the base densi ty t o an a l te rna te condi t i on.

Input Data Commodi t y ...................... General i zed Lube O i 1 T base temperature, 'c ......... 15 t a l te rna te temperature, 'c .... -50.025 P a l te rna te pressure, kpa ...... O Base density, kg/cu m .......... 800.849 volume a t observed t & P ....... 1000


s tep 1 - convert t o cystomary u n i t s t a l te rna te temperature, F .... -58.045 T base, F ..................... 59 P a l ternate, PSI ............... O A l ternate temperature less than -5O'C ( -58 '~ ) - outside l i m i t s o f t a b l e Density less than 800.9 kg/cu m - outside l i m i t s o f tab le

API MPMS 11.1.7.1 Metr ic u n i t s , Example 11 A volume o f a lube o i l i s measured a t observed condit ions o f temperature and pressure. The base density a t 2 0 ' C i s known. ca lcu la te the volume a t base condit ions and cor rec t the base densi ty t o an a l te rna te condi t i on.

Commodi t y ...................... General i zed Lube O i 1 Input Data

T base temperature, 'c ......... 20 t a l te rna te temperature, 'c .... 150.025 P a l ternate pressure, bar ...... 103.43 Base densi t kg/cu m .......... 1163.55 volume a t oke rved t & P .......

t a l te rna te temperature, F .... 302.045

1000


s tep 1 - convert t o cystomary u n i t s

T base, F ..................... 68 P a l ternate, PSI ............... 1500.12538513 Al ternate temperature greater than 150'C (302 '~) - outSide l i m i t s o f tab le Al ternate pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1163.5 kg/cu m - outside l i m i t s o f tab1



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11.1.7.2 Method to Correct Volume and Density from Metric Observed Conditions to Metric Base Conditions


This procedure calculates the density at the metric base conditions (15°C or 20°C and O kPa (gauge)) that is consistent with an observed density measured at the observed temperature and pressure conditions. Because the VCF expressions were developed and expressed in terms of a base density at 60°F, this calculation must be done as a two part process:

1.

2.

Calculate the density at 60°F and O psig consistent with the observed density.

Calculate the density at the metric base temperature and pressure conditions.

The procedure has been written assuming that the input values are all in the proper units (“Cy kPa or bar (gauge), and kg/m3). If they are not in the proper units then apply the procedures in 11.1.5.1. The density values calculated by this procedure are in kg/m3. If these units do not match the original input units, then the calculated density value(s) should be converted to that of the original input value’s units using the procedures in 1 1.1.5.1.

Input Values


a60 Pre-calculated 60°F thermal expansion factor (if commodity group not given)


T

t0

Base temperature (1 5°C or 20°C)

Temperature at which the observed density was measured (“C)

P, Pressure at which the observed density was measured (kPa or bar (gauge))


V, Volume at observed conditions (any valid set of units, such as liters, cubic metres, and barrels)

Output Values

p T Density at metric base conditions (1 5°C or 20°C and O kPa (gauge)) (kg/m3)

CTL Volume correction factor due to temperature

CpL Volume correction factor due to pressure

Fp Scaled compressibility factor (kPa-’ or bar-’)

CTpL Combined volume correction factor due to temperature and pressure


VT Volume at base conditions (same set of units as V )

P60 Density at 60°F and O psig (kg/m3)



--`,,`,,,-`-`,,`,,`,`,,`---


Intermediate Values

E , Base temperature T converted to units of OF (OF)

to.,, Temperature to converted to units of OF (OF)

Pressure Po converted to units of psig (psig)

CTL,,, CTL value correcting p60 to p T

C;L CTL value correcting to the observed temperature

C;pL CTF'L value correcting p60 to the observed temperature and pressure

Fp,psi Scaled compressibility factor (psi-')


Step 1: Convert the base temperature, observed temperature, and observed pressure into customary units using equations in 1 1.1.5.1. Call these variables E , , to;, , and

Step 2: Calculate the correction factors for the density at 60°F, p60 , corresponding to the observed density po at conditions to;, and Po,,i using the procedure in 11.1.6.2. If this procedure returns with an error condition, exit this procedure. There are associated factors that must be adjusted to take into account that the reference temperature is not 60°F and the pressure is not in customary units. Call these factors C;L , CpL , C;PL 9 and FP,psi .

Step 3: Using this value of p60 , calculate the associated metric base density value p T at E , using the procedure in 1 1.1.6.1. The pressure correction need not be calculated since the metric base pressure (O Wa (gauge)) is the same as the base pressure in 1 1.1.6.1 (O psig). Call the CTL associated with this step CTL,60 .

Step 4: Calculate the correction factors for the metric base temperature by combining the correction factors for 60°F. The temperature correction factor is:

G L CTL =- 'TL.60

and the combined temperature and pressure correction factor is:

c,, = c, . CPL .


Modify the scaled compressibility factor for the metric pressure units:

for Wa F',psi F - ' - 6.894757

for bar. F',psi F - ' - 0.06894757



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Step 5: Calculate the volume at the base conditions:

v, = v, . c,,, .




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Example 1

Base temperature. 'c ........... 1 5 t observed temperature. 'c ..... 82.35 P observed pressure. kpa ....... 10005 observed density. kg/cu m ...... 721.1 volume a t observed t & P ....... 10000

Inpu t Data Commodi t y ...................... General i zed Refined product


s tep 1 convert t o customary ? n i t s

t observed temperature F ...... 180.23 T base temperature. F ......... 59 P observed. pressure. ps i ...... 1451.10262769

Correcting observed densi ty t o 6 0 ' ~ & O ps i reference condit ions s tep 2

I terat ion(m) ..... O 1 2 ... 4 Commodity .......... gasoline t r a n s i t i on t r a n s i t i on ... gasol i ne ~ho6O(m) ........... 721.100000000000 771.024002892933 770.371769059203 ... 770.349118751609 KO(m) .............. 192.457100000000 1.48906700000e+03 1.48906700000e+03 ... 192.457100000000 K i i m j ... K2(m) ... A(m) ....

.........

.........

......... B(M) . . . . . . . . . . . . . ~ho6O*(m) ......... a l ha60(m ........ C t ? . 6O(m) ......... d-al pha(m ........ Fp(m) . . . . . . . . . . . . cp l (m) ............ c t p l (m) ........... ~hoGO(m)xctpl. 60(m) d e l t a ~ho6O(m) .... Dt(m) ............. d e l t a Rho(m) ......

E(M) .............. Dp(m) ............. ~hoGO(m+l) ........ Rho60 ............. C t l * ..............

output values ... ...

Fp. ps i ................ cp1 ................... ctp1* .................

o . 243800000000 0 . o00000000000 0.000000000000 -0.001868400000 0.000004868905 0.000004375399 1.522610196760 7.871492061474

721.103510963661 771.027376333242 0.000708209662 0.000636409156 0.913041162555 0.921988714711 1.500000000000 8.500000000000 1.437164972964 1.072840733926 1.021298922143 1.015814216115 0.932487955189 0.936569243501

672.417064487103 722.117367110801 48.682935512897 -1.017367110800 52.207575703224 -1.086270041281

-0.099381547746 -0.064543274367 49.924002892933 -0.652233833730

O . 14 5 122 52 7 5 95 0.730004317792

771.024002892933 770.371769059203

.......... 770.349118751609

. . . . . . . . . 0 . 921444124669 ........ 1.076685418863 ........ 1.015871788215 ........ 0.936069090668

step 3 Correcting 60' F densi

t. F ................. t corrected t o IPTS-68 A ...... B ..... Rho60" a l ha60 de?ta t C t l ... FP? Psi P i n ps cp1 ... ctp1 .. Density C t l . 60 .

...

...

... 'F

...

... ..

...

... kg ....

y t o 15'C base condit ions: ........ 59.000000000000 F ...... 59.006621316269 ........

....................

....................

....................

....................

....................

.................... CU m . a t 15'c ......

0.000004405357 1.506108826170

770.352512411255 0.000640784451

-1.000253583731 1.000640828053 0.658572575399 0.000000000000 1.000000000000 1.000640828053

770.842780077632 1.000640828053

0 . o00000000000 -0.001868400000 0.000004404570 7.832604886721

770.375162118135 0.000640652189 0.921460588472 8.500000000000 1.076555996647 1.015869850080 0.936084029866

721.132710075817

... ~ 0 . 243800000000

... o.ooooa

... o.ooooa

... 0.000640784451

... Ö . 921444124669

... 1.500000000000

... 1.076685418863

... 1.015871788215

... 0.936069090668

... 721.099999086448

Sfep 4 Modify C t l * f a c t o r and ca lcu late Ctp l f a c t o r f o r base temperature o f 15'c

C t l ............................ 0.920854015583 Ctpl ........................... 0.935469615495 c t p l . rounded .................. 0.93547 Fp. kPa ......................... 0.156160024039

... 0.000000913552

step 5 volume a t base condit ions ...... 9354.7



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Example 2

Base temperature, 'c ........... 1 5 t observed temperature, 'c ..... 26.8 P observed pressure, kpa ....... - 5

observed density, kg/cu m ...... 823.7 volume a t observed t & P ....... 1000


Forcing negative pressure t o zero


step 1 convert t o customary ? n i t s

t observed temperature F ...... T base temperature, F ......... P observed, pressure, ps i ......

80.24 59

O

step 2 Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions

I te ra t ion ím) ..... O 1 2 ~ _ _ . _ - Rho6O(m) ........... '8~3.70000Ö000000 832 .O23208166070 832 .O24016649536 Kû(m) .............. 341.095700000000 341.095700000000 341.095700000000 Kl(m) .............. 0.000000000000 0.000000000000 0.000000000000 ~2 (m j .............. o. oooooooooooo 0.000000000000 0.000000000000 A(m) ............... 0.000003456244 0.000003387440 0.000003387433 B i m j ............... ~ho6O*(m) .......... a l pha60(m) ......... Ctl,60(m) .......... d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl, 60(m) del t a ~ho6O(m) ..... Dt(m) ..............

Fp(& ..............

E(M) ...............

2.000000000000 2.000000000000

1.000000000000

Dpimj .............. -o. oooooooooooo -0.000000000000 de l ta Rho(m) ....... 8.323208166070 0.000808483466 ~ho6O(m+l) ......... 832.023208166070 832.024016649536

output values Rho20 .......................... 832.024016649536 C t l ........................... 0.989995461094 Fp,psi ......................... 0.566973846350 cp1 ........................... 1.000000000000 Ctpl* ......................... 0.989995461094

step 3 Correctina 60' F

t, 'F ........... t corrected t o IP A ............... B ...... Rho60" . a l pha60 de l ta t C t l ... FP? Psi P i n ps cp1 ... ctp1 .. Density Ct l ,60

t ... ... ..

...

... kg ...

densitv t o 1 5 ' C base condit ions:

.............. 0.000492721573 .................... -1.000253583731 .................... 1.000492776246 .................... 0.526407914039 .................... 0.000000000000 .................... 1.000000000000 .................... 1.000492776246 CU m , a t 15'c ...... 832.434018321149 .................... 1.000492776246

Sfep 4 Modify C t l * f ac to r and ca

C t l ....................... ctp1 ...................... c t p l , rounded ............. Fp,kPa ....................

1.000000000000 o. 989995461094 823.700000004313

-0.000000004313

culate Ctpl f ac to r f o r base temperature o f 15'c .... 0.989507855128 .... 0.989507855128 .... 0.98951 .... 0.082232607523

step 5 volume a t base condit ions . . .... 989.51



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Commodity ...................... Base temperature. 'c ........... t observed temperature. 'c ..... P observed pressure. kpa ....... observed density. kg/cu m ...... volume a t observed t & P .......

General i zed crude 1 5

1 1 5 722.6

145902

.50

O i 1


s tep 1 convert t o customary p i t s

t observed temperature F ...... -58 T base temperature. F ......... 59 P observed. pressure. ps i ...... 16.6793405482

step 2 Correcting observed densi ty t o 6 0 ' ~ & O ps i reference condit ions

Iterat ion(m) ..... O 1 ~ho6O(m) ........... '722.600000000000 664.214217743108

.............. 341.095700000000 341.095700000000

.............. 0.000000000000

.............. 0.000000000000 .........

B(M) ......... ~ho6O*(m) ... a l ha60(m) . . d-al ha(m) . . cp l (m) ...... c t p l (m) ..... Rho60 (m) xc tp l del t a ~ho6O(m

C t ? . 6O(m) ... Fp(& .......

E(M) ......... Dt(m) ........ m i m i .......

...... 0.000004491036 0.000005315280

...... 2.000000000000 2.000000000000

......

......

......

......

......

......

...... 60 (m) ..... ...... ......

.......

722.603245212681

1.000079548542 1.075110578376 ..............

776.874903934710 -54.274903934710 -50.483089857305 -0.135152229527 -0.000200798113

664.217748214555 0.000773134926 1.088269020951 2.000000000000 0.601186188829 1.000100283948 1.088378156864

d k ì t a Rho(m) ....... -58.385782256892 -0.344324399478 ~hoGO(m+l) ......... 664.214217743108 663.869893343631

output values Rho60 ........... C t l * ............. Fp. ps i ........... cp1 ............. ctp1* ...........

step 3 Correcting 60' F

t corrected t o IP

Rho60* ........... a l ha60 ..........

t. F ........... A ............... B ...............

de?ta t ......

............... 663.869868377549 .............. 1.088357017112 .............. 0.602118682034 .............. 1.000100439513 .............. 1.088466331160

C t l ... FP? Psi P i n ps cp1 ... ctp1 .. Density C t l . 60

density t o 15'C base condit ions: .............. 59.000000000000

.............. -1.000253583731 ........................ 1.000773959950 ........................ 1.134306792464 ....................... 0.000000000000

........................ 1.000000000000

........................ 1.000773959950 kg/cu m , a t 15'c ...... 664.383677067826 ........................ 1.000773959950

2 663.869893343631

0 0 0 0 0 0 0

2.000000000000

1.088466324763 722.600022928389 -0.000022928389

-0.000021064858 -0.155960587255 -0.000300373710 -0.000024966082

663.869868377549

step 4 Modify C t l * f a c t o r and ca lcu late Ctp l f a c t o r f o r base temperature o f 15'C

C t l ............................ 1.087515323806 Ctpl ........................... 1.087624553315 Ctp l . rounded .................. 1.08762 Fp. kPa ......................... 0.087329935201

volume a t base condit ions ...... 158685.93324 step 5

3 663.869868377549 341.095700000000

0.000000000000 0.000000000000 0.000005320796 2.000000000000

663.873400680238 0.000773937176 1.088357017112 2.000000000000 0 . 602118682034 1.000100439513 1.088466331160

722.600000000760 -0.000000000760



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Example 4

Commodi t y ...................... General i zed Refined product Base temperature. 'c ........... 1 5 t observed temperature. 'c ..... 20 P observed pressure. bar ....... 11.25 observed density. kg/cu m ...... 865.6 volume a t observed t & P ....... 99873

Input Data


step 1 convert t o customary p i t s

t observed temperature F ...... 68 T base temperature. F ......... 59 P observed. pressure. ps i ...... 163.167461884

step 2 Correcting observed density t o 60' F &

I terat ion(m) ..... O Commodity .......... ~ho6O(m) ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l pha60(m) ......... C t l . 60(m) .......... d-al ha(m) ......... FD(M'S ..............

_ _ f ue l o i l

0.000003098311 1.307613432453

O ps i reference condit ions 1 2

fue l o i l f ue l o i l 868.036201969593 868. 036119189528 103.872000000000 103.872000000000

0.270100000000 0.270100000000 0.000000000000 0.000000000000 0.000003086948 0.000003086948 1.307015151471 1.307015172741

868.Ö38885551754 868.038798771772 0.000449015417 0.000449015475 0.996403096509 0.996403096038 1.300000000000 1.300000000000 0.485793045037 0.485793167772

Cpì(m) ............. 1.000798960006 1.000793284984 Ctpl(m) ............ 0.997185917889 0.997193528123 ~ho60(m)xctpl, 60(m) 863.164130524430 865.600086769462 de l ta ~ho6O(m) ..... 2.435869475570 -0.000086769462 E(M) ............... 2.442743556515 -0.000087013664 Dt(m) .............. 0.004713986507 0.004696599303 op(mj .............. .o . 002030474931 -0.002004751931 de l ta Rho(m) ....... 2.436205969593 -0.000086780065 RhoGO(m+l) ......... 868.036205969593 868.036119189528

output values Rho20 .......................... 868.036119189528 C t l ........................... 0.996403096038 Fp. ps i ......................... 0.485793167772 cp l ........................... 1.000793285184 Ctpl* ......................... 0.997193527852


t. 'F ........... t corrected t o IP A ............... B ...... Rho60" . a l pha60 de l ta t C t l ... FP? Psi P i n ps cp1 ... ctp1 .. Density C t l . 60

t ... ... ..

...

... kg ...

densitv t o 1 5 ' C base condit ions: .............. 59.000000000000 5-68 'F ...... 59.006621316269 .............. 0.000003086948 .............. 1.307015172741 .............. 868.038798771772 .............. 0.000449015475

.................... -1.000253583731

.................... 1.000449070985

.................... 0.471908186296

.................... 0.000000000000

.................... 1.000000000000

.................... 1.000449070985 CU m . a t 15'c ...... 868.425929024799 .................... 1.000449070985


C t l ....................... ctp1 ...................... c t p l . rounded ............. Fp. bar ....................

step 5 volume a t base condit ions . .

1.000793285184 0 . 997193527852

865.599999997702 0.000000002298


.... 99548.41275



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Example 5

Commodi t y ...................... General i zed Refined product Base temperature. 'c ........... 1 5 t observed temperature. 'c ..... 22.25 P observed pressure. kpa ....... 2587.3 observed density. kg/cu m ...... 817.59 volume a t observed t & P ....... 400.15

Input Data




step 2 Correcting observed density t o 60' F &

I terat ion(m) ..... 0 Commodity ......... ~ho6O(m) .......... KO(m) ............. K1(M) ............. K2(m) ............. A(m) .............. B(M) .............. ~ho6O*(m) ......... a l pha60(m) ........ C t l . 60(m) ......... d-al ha(m) ........ cp l (m) ............ c t p l (m) ........... ~hoGO(m)xctpl. 60(m) de l ta ~ho6O(m) .... Dt(m) .............

Fp(& .............

E(M) ..............

_ _ 817 . 330 .

0 . 0 . 0 . 2.

817 . 0 . 0 . 2. 0 .

j e t fue l 590000000000 301000000000 000000000000 000000000000 000003397074 000000000000 592777407010 00049412 3827 994033739721 000000000000 578919272217

1.002177159928 ..............

0.996197910146 814.481449356498

3.108550643502 3.120414740728 0 . 01202 18 3 19 12

O ps i reference cond

j e t fue l 820.692548571452 330.301000000000

0.000000000000 0.000000000000 0.000003371438 2.000000000000

820.695315478794 0.000490394939 0.994078841829 2.000000000000 0.572669043746 1.002153603876

1

_ _ DD(m) .............. -0.006263285716 -0.006148764741 dé ì tá Rho(m) ....... 3.102548571452 .Ö . ÖÖÖÖ79346639 ~hoGO(m+l) ......... 820.692548571452 820.692469224813

Rho20 .......................... 820.692469224813 C t l ........................... 0.994078840682

output values

Fp. ps i ......................... 0.572669201827 cp l ........................... 1.002153604472 Ctpl* ......................... 0.996219693318


t. ' F ........... t corrected t o IP A ............... B ...... Rho60" . a l pha60 de l ta t C t l ... FP? Psi P i n ps cp1 ... ctp1 .. Density C t l . 60

t ... ... ..

...

... kg ...


.............. 0.000490395034 .................... -1.000253583731 .................... 1.000490449780 .................... 0.546468815042 .................... 0.000000000000 .................... 1.000000000000 .................... 1.000490449780 CU m . a t 15'c ...... 821.094977665680 .................... 1.000490449780


C t l ....................... ctp1 ...................... c t p l . rounded ............. Fp. kPa ....................

i t i o n s

1.002153604472 Ö . 996219693318

817.589999999757 0.000000000243





--`,,`,,,-`-`,,`,,`,`,,`---

SECTION 1 . VOLUME CORRECTION FACTORS FOR CRUDE OILS . REFINED PRODUCTS . & LUBE OILS 1 O0

Example 6

Base temperature. 'c ........... 1 5 t observed temperature. 'c ..... 1.85 P observed pressure. kpa ....... 1835 observed density. kg/cu m ...... 798.9 volume a t observed t & P ....... 1998.7

Input Data Commodi t y ...................... General i zed Refined product




Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions step 2

I terat ion(m) ..... O 1 2 3 Commodity .......... j e t fue l t rans i t i on t rans i t i on t rans i t i on ~ho6O(m) ........... 798.900000000000 787.400070634008 787.384039337631 787.383920775576 KO(m) .............. 330.301000000000 1.48906700000e+03 1.48906700000e+03 1.48906700000e+03 K1(M) .............. 0.000000000000 0.000000000000 0.000000000000 0.000000000000 K2(m) .............. 0.000000000000 -0.001868400000 -0.001868400000 -0.001868400000 A(m) ............... 0.000003557880 0.000003666557 0.000003667230 0.000003667235 B i m j ............... ~ho6O*(m) .......... a l pha60(m) ......... C t l . 60(m) .......... d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl. 60(m) del t a ~ho6O(m) ..... Dt(m) ..............

Fp(& ..............

E(M) ...............

2.000000000000 9.006605007576

1.001437659784 1.014175991955

810.225199972732 -11.325199972732 -11.166898114894

-0 . 02 5012538589

1.001497001104 1.Ö14623246771

798.914416174111 -0.014416174111 -0.014208401155 -0.109477820520

opimj .............. -0.003946878508 -0.004230714297 de l ta Rho(m) ....... -11.499929365992 -0.016031296377 RhoGO(m+l) ......... 787.400070634008 787.384039337631




t ... ... ..

...

... kg ...


.............. 0.000533406248 .................... -1.000253583731 .................... 1.000533459147 .................... 0.615797119674 .................... 0.000000000000 .................... 1.000000000000 .................... 1.000533459147 CU m . a t 15'c ...... 787.803957930685 .................... 1.000533459147



9.005320384922 9.005310885749 787.386926774049 787.386808215474

0.000533405525 0.000533406248 1.013109018441 1.013109036142 8.500000000000 8.500000000000 0.561668867244 0 . 561669106263 1.001497087371 1.001497088009 1.Ö14625731158 1. Öl4625749532

798.900106615004 798.900000786490 -0.000106615004 -0.000000786490 -0.000105078159 -0.109497464438 -0.004231130387 .... ~-~~ .... -0.000118562055

787.383920775576





--`,,`,,,-`-`,,`,,`,`,,`---



Commodity ...................... Base temperature. 'c ........... t observed temperature. 'c ..... P observed pressure. kpa ....... observed density. kg/cu m ...... volume a t observed t & P .......

product



t observed temperature F ...... 41.846

P observed. pressure. ps i ...... 248.014542064

Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions

T base temperature. F ......... 59

step 2

I terat ion(m) ..... O 1 Commodity .......... t rans i t i on gasoline ~ho6O(m) ........... 779.600000000000 769.400165598634

K1(M) .............. 0.000000000000 0.243800000000 K2(m) .............. -0.001868400000 0.000000000000 A(m) ............... 0.000003998615 0.000004413544

~ho6O*(m) .......... a l pha60(m) ......... C t l , 60(m) .......... d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl, 60(m) del t a ~ho6O(m) ..... Dt(m) ..............

KO(m) .............. 1.48906700000e+03 192.457100000000

B(M) ...............

Fp(& ..............

E(M) ............... Dpimj .............. -0.004319297253 -0.004611843291 de l ta Rho(m) ....... -10.199834401366 0.071293846668 ~hoGO(m+l) ......... 769.400165598634 769.471459445302




t ... ... ..

...

... kg ...


.............. 0.000641885641 .................... -1.000253583731 .................... 1.000641929113 .................... 0.660935428188 .................... 0.000000000000 .................... 1.000000000000 .................... 1.000641929113 CU m . a t 15'c ...... 769.965411139556 .................... 1.000641929113



3 gasoline

769.471465004491 192.457100000000

0.243800000000 0.000000000000 0 . 000004412927 1.506393767363

769.47486Ö623165 0.000641885641 1.011614013219 1.500000000000 0.616431370856 1.001531180371 .... ~- ....... ~

1.013162976739 779.599999999564

0.000000000436

-0.004609700597 ö.ööoöö5559i89

769.471465004491





--`,,`,,,-`-`,,`,,`,`,,`---


Example 8 InDut Data

commod; t y . . . . . . . . . . . . . . . . . . . . . . Base temperature, 'c ........... 1 5 Alpha a t 6 0 ' ~ per ' F ........... 0.0005763 t observed temperature. 'c ..... 29.18

Speci a l i zed L i qu i d

P observed pressure, kpa . . . . . . . 395 observed densi ty , kg/cu m ...... 853.7 volume a t observed t & P ... .... 8501.3


s tep 1 convert t o customarv u n i t s

t observed temperaturé ' F ...... 84.524 T base temperature, F ......... 59 P observed, pressure, p s i ...... 57.2899088394

s tep 2 Correct ing observed dens i ty t o 6 0 ' ~ & O p s i reference condi t ions

I terat ion(m) . . . . . O 1 2 ~ho6O(m) ........... 853.700000000000 865.737133188744 865.736878409727 ~hoGO*(m) ... ...... 853.703382379864 865.740563260019 865.740308479993 Ctl,6O(m) ... ...... 0.985804899058 0.985804899058 0.985804899058 d-al ha(m) .. ...... 0.000000000000 0.000000000000 0.000000000000 FD(M'S . . . . . . . . . . . . . 0.515952255703 _ _ _ _ _ _ 1.000306987389 1.000295675745 1.000295675975

o. 535684525741 O . 515951854357 . . . - . . . - - - .

. . . . . . 0.986107528730 0.986096377657 0.986096377884 60(m) 841.839997277023 853.700251040320 853.700000000005 ..... 11.860002722977 -0.000251040320 -0.000000000005

E(M) ......... Dt(m) ........

...... 12.027088707301 -0.000254579903

...... 0.000000000000 0.000000000000 Dp(m j -0.000781516392 d e l t a Rho(m) ....... 12.037133188744 -0.000254779017

. . . . . . . . . . . . . . -o. 000834457947

~hoGO(m+l) ......... 865.737133188744 865.736878409727 output values

Rho20 .......................... 865.736878409727 C t l ........................... 0.985804899058

c p l ............................ 1.000295675975 Ctp l * ........... .............. 0.986096377884

Fp,psi ......................... 0.515952255703

s tep 3 Correct ina 60' F

t, ' F ........... t corrected t o IP Rho60* .......... a l ha60 . . . . . . . . . . de?ta t ...... C t l ... FP? Psi P i n ps cp1 ... ctp1 .. Density Ct l ,60

sTe Modi f

C t l .... C t D 1 .. .

....

... ..

...

... kg .... 4

densi tv t o 15'C base condi t ions: .............. 59.000000000000 5-68 ' F ...... 59.006621316269 .............. 865.740308479993 .............. 0.000576300000

............... 1.000576349988 .............. -1.000253583731

.....

.................... 0.475019162473

.................... 0.000000000000

.................... 1.000000000000 .... 1.000576349988 .... 866.235845849433 .... 1.000576349988

................ CU m , a t 15'c .. ................

C t l * f a c t o r and ca ................... ...................

c t p l , rounded . . . . . . . . . . . . . Fp,kPa ....................

s tep 5 volume a t base condi t ions . .

cu la te Ctp l f a c t o r f o r base temperature o f 15'c .... 0.985237057692 .... 0.985528368620 .... 0.98553 .... 0.074832551126

.... 8378.286189



--`,,`,,,-`-`,,`,,`,`,,`---


Example 9

Commodi t y ...................... General i 1 zed Lube O i Base temperature. 'c ........... 1 5 t observed temperature. 'c ..... -49.97 P observed pressure. bar ....... 3 1 . 1 observed density. kg/cu m ...... 1204.6 volume a t observed t & P ....... 100

Input Data



t observed temperature F ...... -57.946 T base temperature. F ......... 59 P observed. pressure. ps i ...... 451.067383521

Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions Note. Rho60 has been l i m i t e d t o the maximum tab le value i n one o r more cases .

step 2

I terat ion(m) ..... O ~ho6O(m) ........... 1.16350000000e+03 KO(m) .............. 0.000000000000 K1(M) .............. 0.348780000000 K2(m) .............. 0.000000000000

ddai Dhä(m) ......... 1.000000000000

0.000000000000 0.000002062240 A(m)- ............... 0 . 000002060874

~ho6O*(m) .......... 1.16350239783e+03 1.16273180517e+03 B(M) ............... ~.oooooooooooo i: ööööööööööoö a l ha60(m) ......... 0.000299767324 0.000299965993

1.000000000000 Ct?.6O(m) .......... 1.034960505816 1.034983389675

2 1.16272940184e+03 0.000000000000 0.348780000000 0.000000000000 0.000002062240 i: ööööööööööoö 1.16273179967e+03 0.000299965994 1.034983389839 1.000000000000 . . . .

.............. 0.219674012573 0.219815870301 0.219815871316

. . b23831696 -0.000005508255 E(M) ............... -0.744144279942 -0.000005316794 Dt(m) .............. .o . 033356241627 -0.033377021810 Dp(m) .............. -0.000965881756 -0.000967787625 de l ta Rho(m) ....... -0.770592656165 -0.000005505893 ~ho6O(m+l) ......... 1.16272940734e+03 1.16272940184e+03

output values Rho60 .......................... 1.16272940184e+03

Fp. ps i .......... cp1 ............. ctp1* ...........


t corrected t o IP

Rho60* ...........

t. F ........... A ................ B ................

.....

.....

.....

densi ..... 5-68 ...... ...... ......

C t l * ........................... 1.034983389839 ........ 0.219815871316 ........ 1.000992501782 ........ 1.036010612698

y t o 1 5 ' C base condit ions: ........ 59.000000000000 F ...... 59.006621316269 ........ 0.000002062240 ........ 1.000000000000 ........ 1.16273179967e+03

a l ha60 ........................ 0.000299965994 de?ta t . O F .................... -1.000253583731 C t l ............................ 1.000300016026 Fp. ps i ......................... 0.273073437320 P i n ps i ....................... 0.000000000000

Ctpl ........................... 1.000300016026 Density. kg/cu m . a t 1 5 ' C ...... 1163.078239292499 C t l . 60 ......................... 1.000300016026

cp1 ............................ 1.000000000000


C t l ....................... ctp1 ...................... c t p l . rounded ............. Fp. bar ....................

volume a t base condit ions . step 5

culate c t D 1 f ac to r f o r base temera ture o f 15'c .... l'.O34672971366 .... 1.035699886134 .... 1.03570 .... 3.188159804848

.... 103.57



--`,,`,,,-`-`,,`,,`,`,,`---


Example 10

Base temperature. 'c ........... 1 5 t observed temperature. 'c ..... 150 P observed pressure. kpa ....... 100 observed density. kg/cu m ...... 734.3 volume a t observed t & P ....... 987.37

Input Data Commodi t y ...................... General i 1 zed Lube O i



t observed temperature F ...... 302 T base temperature. F ......... 59 P observed. pressure. ps i ...... 14.5037743897

Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions Note. Rho60 has been l i m i t e d t o the minimum tab le value i n one o r more cases .

step 2

I terat ion(m) ..... 0 ~ho6O(m) ........... 800.900000000000 KO(m) .............. 0.000000000000 K1(M) .............. 0.348780000000 K2(m) .............. 0.000000000000 A(m)- ............... 0 . 000002993915 B(M) ............... ~.oooooooooooo ~hoGO*(m) .......... 800.902397828986 a l ha60(m) ......... 0.000435483775 Ct?.6O(m) .......... 0.891989089232 ddai Dhä(m) ......... 1.000000000000

1 820.631387494658

0.000000000000 0.348780000000 0.000000000000 0.000002921929

1.000000000000 _ _ Fe(mj .............. 1.460680703550 1.307424930168 cp l (m) ............. 1.000211898725 1.000189661927 Ctpl (m) ............ 0.892178100583 0.894800173950 ~ho60(m)xctpl, 60(m) 714.545440757119 734.301108279052 de l ta ~ho6O(m) ..... 19.754559242881 -0.001108279052 _ _ E(M) ............... 22.141945907400 -0.001238577153 D t í m ) .............. 0.123157370141 0.119779166844 Dpimj .............. .ö . Öö098864ji66 .ö . 000842856189 de l ta Rho(m) ....... 19.731387494658 -0.001106923728 ~ho6O(m+l) ......... 820.631387494658 820.630280570930

output values Rho60 .......................... 820.630280570930

Fp. ps i .......... cp1 ............. ctp1* ...........


t corrected t o IP

Rho60* ...........

t. F ........... A ................ B ................

.....

.....

.....

densi ..... 5-68 ...... ...... ......

C t l * ........................... 0.894630352025 ........ 1.307432768085 ........ 1.000189663064 ........ 0.894800030358

y t o 15'C base condit ions: ........ 59.000000000000 F ...... 59.006621316269 ........ 0.000002921933 ........ 1.000000000000 ........ 820.632678399864

a l ha60 ........................ 0.000425013540 de?ta t . O F .................... -1.000253583731 C t l ............................ 1.000425069038 Fp. ps i ......................... 0.546584015650 P i n ps i ....................... 0.000000000000

Ctpl ........................... 1.000425069038 Density. kg/cu m . a t 15'C ...... 820.979105094945 C t l . 60 ......................... 1.000425069038

cp1 ............................ 1.000000000000



volume a t base condit ions . step 5

2 820.63028Ö570930

0.000000000000 0.348780000000 0.000000000000 0.000002921933

1.307432768085

culate Ctpl f ac to r f o r base temperature o f 15'c .... 0.894250233938 .... 0 . 894419840177 .... 0.89442 .... 0.189627098980

.... 883.1234754



--`,,`,,,-`-`,,`,,`,`,,`---


Example 11

Base temperature, 'c ........... 15 t observed temperature, 'c ..... -50.05 P observed pressure, kpa ....... O observed density, kg/cu m ...... 470.27 volume a t observed t & P ....... 1000




t observed temperature F ...... -58.09 T base temperature, F ......... 59 P observed, pressure, ps i ...... O observed temperature less than -5O'C ( -58 '~ ) - outside l i m i t s o f t a b l e Density less than 470.4 kg/cu m - outside l i m i t s o f tab le

Example 12

Base temperature, 'c ........... 15 t observed temperature, 'c ..... 150.03 P observed pressure, bar ....... 103.425 observed density, kg/cu m ...... 1201.85 volume a t observed t & P ....... 1000




t observed temperature F ...... 302.054 T base temperature, F ......... 59 P observed, pressure, ps i ...... 1500.05286626 observed temperature greater than 150'C (302 '~) - outSide l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1201.8 kg/cu m - outside l i m i t s o f t a b l e

Example 13

Base temperature, 'c ........... 15 t observed temperature, 'c ..... -50.05 P observed pressure, kpa ....... O observed density, kg/cu m ...... 470.17 volume a t observed t & P ....... 1000

Input Data Commodity ...................... Generalized Ref

computed Data - l a s t d i g i t i s rounded f o r d isp

ned product

ay purposes


t observed temperature F ...... -58.09 T base temperature, F ......... 59 P observed, pressure, ps i ...... O observed temperature less than -5O'C ( -58 '~ ) - outside l i m i t s o f t a b l e Density less than 470.3 kg/cu m - outside l i m i t s o f tab le



--`,,`,,,-`-`,,`,,`,`,,`---


Example 14

Base temperature, ‘c ........... 1 5 t observed temperature, ‘c ..... 150.02 P observed pressure, kpa ....... 10342.5 observed density, kg/cu m ...... 1209.56 volume a t observed t & P ....... 1000




t observed temperature F ...... 302.036 T base temperature, F ......... 59 P observed, pressure, ps i ...... 1500.05286626 observed temperature greater than 150’C (302’~) - outside l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1209.5 kg/cu m - outside l i m i t s o f t a b l e

Example 1 5

Base temperature, ‘c ........... 1 5 t observed temperature, ‘c ..... 15.56 P observed pressure, kpa ....... 10342.5 observed density, kg/cu m ...... 1208.52 volume a t observed t & P ....... 1000

Inpu t Data Commodi t y ...................... General i zed Lube O i 1



t observed temperature F ...... 60.008 T base temperature, F ......... 59 P observed, pressure, ps i ...... 1500.05286626 observed pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1208.3 kg/cu m - outside l i m i t s o f t a b l e

Example 16

Commodi t y ...................... General i zed Lube O i 1 Base temperature, ‘c ........... 1 5 t observed temperature, ‘c ..... 22.42 P observed pressure, kpa ....... O observed density, kg/cu m ...... 714.245 volume a t observed t & P ....... 1000

Inpu t Data



t observed temperature F ...... 72.356 T base temperature, F ......... 59 P observed, pressure, ps i ...... O Density less than 714.3 kg/cu m - outside l i m i t s o f tab le



--`,,`,,,-`-`,,`,,`,`,,`---


Example 1 7

Commodi t y . . . . . . . . . . . . . . . . . . . . . . Base temperature, 'c ........... 1 5 t observed temperature, 'c ..... 0.42 P observed pressure, kpa ....... O observed density, kg/cu m ...... 723.45 volume a t observed t & P ... .... 1000

Input Data General i zed Lube O i 1



t observed temperature F ...... 32.756 T base temperature, F ......... 59 P observed, pressure, ps i . . . . . . O

step 2 Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions Note, Rho60 has been l i m i t e d t o the minimum tab le value i n one o r more cases.

KO(m) ....... K1(M) ....... K2 (III) . . . . . . .

Iterat ion(m) . . . . . O 1 2 ~ho6O(m) ........... 800.900000000000 800.900000000000 800.900000000000

0.000000000000 0.000000000000 0.000000000000 0.348780000000 0.348780000000 0.348780000000 0.000000000000 0.000000000000 0.000000000000

A(m)- . . . . . . . . B(M) ........ ~ho6O*(m) ... a l ha60(m) . . Ct?,6O(m) . . . d-alpha(m) . . cpl(m) ...... Fp(m) . . . . . . . c t p l (m) . . . . . Rho60 (m) xc tp l del t a ~ho6O(m

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . . ...... ...... 60 i i j . ..

E(M) ......... .... D t (i) . . . . . . . . . . . Dp(m) ........... de l ta Rho(m) . . . . ~hoGO(m+l) ......

convergence not Density i s outs

... .. .. .. .. .. ach de

... 14 ...

. . . 800.9000ö0000000

... 0.000000000000

... 0.348780000000

... 0.000000000000 0.000002993915 0.000002993915 0.000002993915

1.000000000000 1.000000000000 1.000000000000

... 0.000002993915

800.902397828986 800.902397828986 800.902397828986 ... 800.902397828986 0.000435483775 0.000435483775 0.000435483775 ... 0.000435483775 1.011823984996 1.011823984996 1.011823984996 ... 1.011823984996

... 1.000000000000

i: öööööööööööö i: öööööööööööö i: öööööööööööö . . . 1.000000000000

0.530563546266 0.530563546266 0.530563546266 1.000000000000 1.000000000000 1.000000000000 1.011823984996 1.011823984996 1.011823984996

810.369829583667 810.369829583667 810.369829583667 -86.919829583667 -86.919829583667 -86.919829583667 -85.904100784852 -85.904100784852 -85.904100784852 -0.011639100638 -0.011639100638 -0.011639100638 -0.000000000000 -0.000000000000 -0.000000000000 _ . _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _

0.000000000000 0.000000000000 0.000000000000 800.900000000000 800.900000000000 800.900000000000

eved a f t e r 1 5 i t e ra t i ons , so lu t ion not found i m i t s o f procedur

... 0.530563546266

... 1.000000000000

. . . 1.011823984996

. . . 810.369829583667

... -86.919829583667

... -85.904100784852

... -0.011639100638 ...__ ~~~

... -0.000000000000

... 0.000000000000

... 800.900000000000



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.7.3 Method to Correct Volume and Density from Observed Metric Conditions to Alternate Metric Conditions


This procedure combines those in 1 1.1.6.2 and 1 1.1.6.1. The density at conditions of 60°F and O psig that is consistent with the observed density is first calculated. This density is then corrected to the alternate temperature and pressure conditions. The corresponding density at the metric base temperature (1 5°C or 20°C) is also calculated.

The procedure has been written assuming that the input values are all in the proper units (“Cy kPa or bar (gauge), and kg/m3). If they are not in the proper units then apply the procedures in 11.1.5.1. The density values calculated by this procedure are in kg/m3.

Input Values

Commodity group describing liquid (if a60 not input)

a 6 0 Pre-calculated 60°F thermal expansion factor (if commodity group not given)

V, Volume at observed conditions (any valid set of units, such as liters, cubic metres, and barrels)


t0 Temperature at which the observed density was measured (“C)

P, Pressure at which the observed density was measured (kPa or bar (gauge))

t

P

T

Alternate temperature at which density is desired (“C)

Alternate pressure at which density is desired (kPa or bar (gauge))

Base temperature (1 5°C or 20°C)

Output Values

P Density at alternate conditions t and P (kg/m3)

p T Density at base temperature conditions T and O psig (kg/m3)

CTL,o Volume correction factor due to temperature between the base and observed temperatures

CpL,o Volume correction factor due to pressure between the base and observed pressures at the observed temperature

Scaled compressibility factor at the observed temperature (kPa-’ or bar-’) FP,o

CTpL,o Combined volume correction factor due to temperature and pressure between the base and observed conditions

CTL Volume correction factor due to temperature between the base and alternate temperatures

CpL Volume correction factor due to pressure between the base and alternate pressures at the alternate temperature

Scaled compressibility factor at the alternate temperature (Ha-’ or bar-’) Fp



--`,,`,,,-`-`,,`,,`,`,,`---

SECTION 1 - VOLUME CORRECTION FACTORS FOR CRUDE OILS. REFINED PRODUCTS. & LUBE OILS 1 o9

CTpL Combined volume correction factor due to temperature and pressure between the base and alternate conditions


V Volume at alternate conditions t and P (same units as V , )

VT Volume at base conditions (same set of units as V )

p60 Density at 60°F and O psig (kg/m3)

Intermediate Values

E , Base temperature T converted to units of OF (OF)

to,oF Density measurement temperature to converted to units of OF (OF)

P,,,i Density measurement pressure Po converted to units of psig (psig)

to, Alternate temperature t converted to units of OF (OF)

Ppsi Alternate pressure P converted to units of psig (psig)

CTL,,O CTL value correcting &O to p T

C;L,o CTL value correcting p60 to the observed temperature

C;pL,o CTPL value correcting p60 to the observed temperature and pressure

FP,o,psi Scaled compressibility factor at observed temperature (psi-')

C;L CTL value correcting to the alternate temperature

C;pL CTPL value correcting p60 to the alternate temperature and pressure

Fp,psi Scaled compressibility factor at alternate temperature (psi-')


Step 1: Convert the base temperature, density measurement temperature and pressure, and alternate temperature and pressure into customary units using equations in 11.1.5.1. Call these variables E , , to,.,, , Po,psi, to,,

and Pps.

Step 2: Calculate the density at 60°F, , corresponding to the observed density po at conditions to;, and Po,,i using the procedure in 11.1.6.2. If this procedure returns with an error condition, exit this procedure. There are associated factors that must be adjusted to take into account that the reference temperature is not 60°F and the pressure is not in customary units. Call these factors c;L,o , C,,,, , c;pL,o , and Fp,o,psi.

Step 3: Using this value of from Step 2, calculate the correction factors for the density p at the alternate temperature and pressure to, and Ppsi using the procedure in 11.1.6.1. If this procedure returns with an error condition, exit this procedure. There are associated factors that must be adjusted to take into account



--`,,`,,,-`-`,,`,,`,`,,`---


Step 4:

Step 5:

Step 6:

Step 7:

that the reference temperature is not 60°F and the pressure is not in customary units. Call these factors C & , 3 C p L 3 Cí$L 3 and F p , p s i .

Using the value of &o from Step 2, calculate the associated metric base density value p T at E , using the procedure in 1 1.1.6.1. The pressure correction need not be calculated since the metric base pressure (O Wa (gauge)) is the same as the base pressure in 11.1.6.1 (O psig). Call the CTL associated with this step ‘TL,60 .

Calculate the correction factors for the metric base temperature by combining the correction factors for 60°F. The temperature correction factors are:

and the combined temperature and pressure correction factors are:

c,, = c, . CPL .

Round these values of C,,,, and C,, consistent with 1 1.1.5.4.

Modify the scaled compressibility factor for the metric pressure units:

1 FP,o,psi

FP,psi

6.894757 for wa FP,o =

F - - 6.894757

1 FP,o,psi

FP,psi

0.06894757 for bar FP,o =

F - - 0.06894757

Calculate the volumes at the base conditions:

and at the alternate conditions t and P:

V = - VT

CTPL

Exit from this procedure.



--`,,`,,,-`-`,,`,,`,`,,`---



I npu t Data Commodity ...................... Generalized crude O i l t observed. 'C ................. 26.82 P observed.pressur$, kpa ....... - 5 Base temperature. c ........... 1 5 t a l ternate temp. 'C ........... 90 P a l ternate pressure. kpa ...... O

observed densi ty. kg/cu m ...... 823.687 Forcing negative pressure(s1 t o zero

volume a t observed t & P ....... 1247.65


step 1 Convert t o customary u n i t s

T base. F ..................... 59 t observed. 'F ................. 80.276 t a l ternate temperature. 'F .... 194 P observed pressure. PSI ....... O P a l ternate pressure. PSI ...... O

step 2 Correct ing observed densi ty t o 60'F & O ps i reference condi t ions

I terat ioním) ..... 0 1 ~ho6O(m) ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) ......... C t ? . 6O(m) .......... d-al pha(m) ......... Fp(m) .............. cpl (m) ............. c t p l (m) ............ ~hoGO(m)xctpl. 60(m) del t a ~ho6O(m) ..... Dt(m) .............. de l ta Rho(m) .......

E(M) ............... Dp(m) .............. ~hoGO(m+l) .........

output values Rho60 ........... C t l .o ........... cp1 .o ........... ctp1 .o .......... Fp.0. ps i ........

SteD 3 Cor re i t i ng 60' F

t corrected t o IP t. F ........... A ............... B ...... Rho60" . a l ha60 de?ta t C t l * . . FP? Psi P i n ps cp1 ... ctp1* . Density

0.000003456353 2.000000000000

823.689846945966 0.000502746226 0.989773108757 2.000000000000 0.583626059244 1.000000000000 0.989773108757

815.263242632906 8.423757367094 8.510796355814 0.020719880670

-0.000000000000 8: 338033300798

832.025033300798

832. 025033300798 341.095700000000

0.000000000000 0.000000000000 0.000003387425 2.000000000000

0.567043227602 1.000000000000

0 . 020300182163 -0.000000000000 0: 000812920720

832.025846221517

.............. 832.025846221517

.............. 0.989977659642

.............. 0 . 567041657958

.............. 1.000000000000

.............. 0.989977659642

and O ps i densi ty t o a l ternate condi t ions: .............. 194.000000000000 5-68 'F ...... 194.041903907457 .............. 0.000003387418 .............. 2.000000000000 .............. 832.028664634558 .............. 0.000492719406

t .................... 134.035029007457 ........................ 0.932831011404 ........................ 0.843798579721 ....................... 0.000000000000

........................ 1.000000000000

........................ 0.932831011404 a t t & P, kg/cu m ...... 776.139511645102

step 4 Correct inq 60' F densi .

t. 'F ................. A ..................... B ..................... t corrected t o IPTS-68

Rho60* ................ a l ha60 ............... C t l ................... Fp. ps i ................ de?ta t. ...........

y t o 1 5 ' C ........ F ...... ........ ........ ........ ........

base condi t i ons : 59.000000000000 59.006621316269 0.000003387418 2.000000000000

832.028664634558 0.000492719406

-1.000253583731 1.000492774079

........ 0 . 526404800069

2

0.00000338



--`,,`,,,-`-`,,`,,`,`,,`---


P i n ps i ....................... 0.000000000000

Ctpl ........................... 1.000492774079 Density. kg/cu m. a t i S ' C / O kpa 832.435846991832 C t l . 60 ........................ 1.000492774079

cp1 ............................ 1.000000000000

Sfep 5 Modifv C t l * f ac to r and ca

C t l . o ..................... C t l ....................... ctp1. o .................... C t D 1 .o. rounded ............ ctp1 . . ............. Ctpl . rounded ...... Fp.0. kPa .......... Fp. kPa ............

volume a t base cond volume a t a l te rna te

step 6

........

........

culate the C t D 1 f ac to r f o r 1 5 ' C base condit ions: .... 0.989&90064587 .... 0.932371562866 .... 0.989490064587 .... 0.98949 .... 0.932371562866 .... 0.93237

............ 0.082242442766

............ 0.122382642306

ti ons ...... 12 34.5 37198 500 condi t i ons . 1324.085071914



--`,,`,,,-`-`,,`,,`,`,,`---


Example 2

t observed. 'C ................. -40

Base temperature. c ........... 1 5 t a l te rna te temp. 'C ........... 90 P a l ternate pressure. bar ...... 24.35 observed density. kg/cu m ...... 758.7 volume a t observed t & P ....... 1000


P observed pressure. bar ....... 2.15



T base. F ..................... 59 t observed. 'F ................. -40 t a l te rna te temperature. 'F .... 194 P observed pressure. PSI ....... 31.1831149379 P a l ternate pressure. PSI ...... 353.16690639

step 2 Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions

-I terat ion(m) ...... 0 ~ho6O(m) ........... 758.700000000000 KO(m) .............. 341.095700000000 K i i m j .............. o . oooooooooooo K2(m) .............. 0.000000000000 A(m) ............... 0.000004073825 B(M) ............... 2.000000000000 ~hoGO*(m) .......... 758.703090801856 al~ha60(m) ......... 0.000592560281 c t i .60( i i. .......... d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl. 60(m) del t a ~ho6O(m) ..... Dt(m) .............. de l ta Rho(m) .......

Fp(& ..............

E(M) ............... Dp(m) .............. ~hoGO(m+l) .........

outout values

1.058083142973 2 : öööööööoööoö 0.457240895647 1.000142602287 1.058234028049

802.882157080785 -44.182157080785 -41.75Ö8376311Ö5 -0.107275970307 -0.000347264176

-46.786110132457 711.913889867543

1 711.913889867543 341.095700000000

0.000000000000 0.000000000000 0.000004626873 2.000000000000

711.917183791842 0.000673003454 1.065762254490 2.000000000000 0.539420913206 1.000168236542 1.065941554646

758.858598539479 -0.158598539478 -0.148787275238 -0.120106813994 -0.000465306440 -0.169186443476

711.744703424067 .... ......

Rho6Or; ......................... 711.744696439390 C t l , o .......................... 1.065792692608 FD.O.DSi ....................... 0.539775702959 cpi . ó' .......................... 1.000168347214 c t p l . o ......................... 1.065972115838


t. F .......................... 194.000000000000 t corrected t o IPTS-68 'F ...... 194.041903907457 A .............................. 0.000004629073 B .............................. 2.000000000000 Rho60* ......................... 711.747991146704 alpha60 ........................ 0.000673323457 de l ta t . 'F .................... 134.035029007457

.............. 0.907768859462

.............. 1.631503749170 C t l * ............. Fp. ps i ........... P i n ps i ........ cp1 ............. ctp1* ........... Density a t t & P.


t corrected t o IP

Rho60* ...........

t. F ........... A ................ B ................

.............. 353.166906389884

.............. 1.005795323575

.............. 0.913029673734 kg/cu m ...... 649.844027971673

density t o 1 5 ' C base condit ions: .............. 59.000000000000 5-68 'F ...... 59.006621316269 .............. 0.000004629073 .............. 2.000000000000 .............. 711.747991146704

a l ha60 ........................ 0.000673323457 de?ta t . O F .................... -1.000253583731 C t l ............................ 1.000673362920 FD.DS~ ......................... 0.861873048137 . . . P i n ps i ....................... 0.000000000000

Ctpl ........................... 1.000673362920 Density. kg/cu m . a t i S ' C / O bar 712.223958926801

cp1 ............................ 1.000000000000

2 711.744703424067 341.095700000000

0.000000000000 0.000000000000 0.000004629073 2.000000000000

711.747998131348 0.000673323444 1.065792691351 2.000000000000 0.539775688302 1.000168347209 1.065972114576

758.700006547377

3 711.744696439390 341.095700000000

0.000000000000 0.000000000000 0.000004629073 2.000000000000

711.747991146704 0.000673323457 1.065792692608 2.000000000000 0.539775702959 1.000168347214 1.065972115838

758.700000000175 -0.000000000175



--`,,`,,,-`-`,,`,,`,`,,`---


C t l . 60 ......................... 1.000673362920

Sfep 5 Modify C t l * f a c t o r and ca lcu la te the Ctpl f a c t o r f o r 15'C base condit ions:

c t 1 . o .......................... 1.065075510252 7 - ~~~~~~~~~~~

_ - C t l ............................ 0.907158012893 ctp1.o ......................... 1.065254812747 ctp1.o . rounded ................ 1.06525 c t p l ........................... 0.912415287111 c t p l . rounded .................. 0.91242 ~ p . 0 . bar ....................... 7.828785016773 p. bar ......................... 23.662962293959

vol Ume a t base condit ions ...... 1065.250000000 volume a t a l te rnate condit ions . 1167.499616405

step 6



--`,,`,,,-`-`,,`,,`,`,,`---


Example 3

Commodity ...................... Generalized crude O i l t observed. 'C ................. 26.82

- 5 Base temperature. c ........... 20 t a l ternate temp. 'C ........... 68.45 P a l ternate pressure. kpa ...... O

Observed densi ty. kg/cu m ...... 823.687

Inpu t Data

P observed pressure. kpa .......

Forcing negative pressure(s) t o zero

....... volume a t observed t & P 243.85



T base. F ..................... 68 t observed. 'F ................. 80.276 t a l ternate temperature. 'F .... 1 5 5 . 2 1 P observed pressure. PSI O P a l ternate pressure. PSI ...... O

.......

step 2 Correct ing observed

I t e r a t i o n Rho60(m) ........... Kû(m) .............. Kï(m) .............. Kï(m) .............. A(m) ............... B(M) ............... Rho60*(m) .......... a l ha60(m) ......... C t ? 60(m) .......... d-ai pha(m) ......... Cpl (m) ............. Ctpl (m) ............ Rho60(m)xctplI 60(m) del t a ~ho6O(m) .....

Fp(m) ..............

E(M) ............... Dt(m) .............. Dp(m) .............. de l ta Rho(m) ....... Rho60(m+l) .........

Output values Rho60 .......................... Fp.0. ps i ....................... C t l . o .......................... cp1. o .......................... ctp1. o .........................

step 3 Correctina 6 0 ' ~ and O mi dens

t. 'F .......................... A .............................. B .............................. Rh060" ......................... a l ha60 ........................ de?ta t. 'F .................... C t l " ........................... Fp. ps i ......................... P i n ps i ....................... cp1 ............................ ctp1* .......................... Density a t t & P . kg/cu m ......

t corrected t o IPTS-68 'F ......

O psi reference condi t ions . I L

832.025033300798 832.025846221517 341.095700000000 341.095700000000

0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000003387425 0. 000003387418 2.000000000000 2.000000000000

832.027851716592 832.028664634558 0.000492720369 0.000492719406 0.989977640002 0.989977659642 2.000000000000 2.000000000000 0.567043227602 0.567041657958

0.000829423158 0.020300182163 ..............

-0.000000000000 0 . 000812920720

832.025846221517

832.025846221517 0.989977659642 0.567041657958 1. ööööoööööööö 0.989977659642

t y t o a l ternate con 155.210000000000 155.242076384128

0.000003387418 2.000000000000

832.028664634558 0.000492719406

95.235201484128 0.952480168160 0.736816285394 0.000000000000 1.000000000000 0.952480168160

792.488117922186

step 4 Correct ing 60' F densi ty t o 20'C base conditions:

t. F .......................... 68.000000000000 t corrected t o IPTS-68 'F ...... 68.008921288340 A .............................. 0.000003387418

Rho60* ......................... 832.028664634558 a l ha60 ........................ 0.000492719406

8 . 002046388340 C t l ............................ 0.996052590368 Fp. ps i ......................... 0.543226596368 P i n ps i ....................... 0.000000000000 cp1 ............................ 1.000000000000 Ctpl ........................... 0.996052590368

B .............................. 2.000000000000

de?ta t . O F ....................

id t ions:



--`,,`,,,-`-`,,`,,`,`,,`---


Density, kg/cu m , a t 2O'C/O kpa 828.741499381895 Ct1,60 ......................... 0.996052590368

Sfep 5 Modify C t l * f a c t o r and ca

C t 1 , O ..................... C t l ....................... C t D l . 0 ....................

culate the Ctpl f a c t o r f o r 20'C base condi t ions: .... 0.993900994000 .... 0.956254897955 .... 0.993900994000

Ctpl ;o, rounded . . . . . . . . . . . . . . . O. 99390 Ctpl ...................... .... 0.956254897955 Ctp l , rounded ..... ............ 0.95625

............ 0.082242442766

............ 0.106866171700 Fp-,o, kpa . . . . . . . . . . Fp,kPa ............

volume a t base cond volume a t a l ternate

step 6 t i ons ...... 242.362515000 condi t ions . 253.450996078



--`,,`,,,-`-`,,`,,`,`,,`---



Commodi t y ...................... General i zed Refined Product t observed. 'C ................. 22.25

2585 Base temperature. c ........... 1 5 t a l ternate temp. 'C ........... 102.35 P a l ternate pressure. kpa ...... 3505 Observed densi ty. kg/cu m ...... 817.55 volume a t observed t & P ....... 9987.5




T base. F ..................... 59 t observed. 'F ................. 72.05 t a l ternate temperature. 'F .... 216.23 P observed pressure. PSI ....... 374.922567974 P a l ternate pressure. P S I ...... 508.35729236

step 2 Correct ing observed densi ty t o 60'F & O ps i reference cond

I terat ioním) ..... O 1 Commodity ...... Rho60(m) ....... Kû(m) .......... Kï(m) .......... Kï(m) .......... A(m) ........... B(M) ........... Rho60*(m) ...... a l ha60(m) ..... C t ? 60(m) ...... d-aipha(m) ..... Cpl (m) ......... Ctpl (m) ........ Rho60(m)xctpl. 60 de l ta ~ho6O(m) .

Fp(m) ..........

E(M) ........... Dt(m) .......... Dp(m) .......... de l ta Rho(m) ... Rho60(m+l) .....

Output values Rho60 .......... C t l .o .......... Fp.0. ps i ....... cp1 .o .......... ctp1 .o .........

....

....

....

....

....

....

....

....

....

....

....

....

....

.... ' ( m l .... .... .... .... .... .... ..... ..... ..... ..... .....

. . i e t f ue l

817 . ~SÖOOÖÖOOOOO 330.301000000000

0.000000000000 0.000000000000 0.000003397406 2.000000000000

1.002175527183 0.996195701022

814.439795370921 3.110204629079 3.122081962296 O . 012023019412

-0.006259201048 3.1Ö4189975112

820.654189975112

i e t fiel

0.000003371753 2: öööööööööööö

820.656957011782 0.000490440783 0.994078287334 2.000000000000

i t ions 2

j e t f üe l 820.654110634883 330.301000000000

0.000000000000 0.000000000000

2.0000000000ö0 0.572745475182 0.572745633293 1.002151973087 1.002151973683 0 . 5 99621751705 0 . 9962 17 5 16497

817.550079497508 817.549999999757 -0.000079497508 0.000000000243 -0.000079799347 0.011931385668 ..............

-0.006144683052 -0.000079340229

820.654110634883

........... 820.654110634883

........... 0.994078286187

........... 0.572745633293

........... 1.002151973683

........... 0.996217516497


t. F .......................... 216.230000000000 t corrected t o IPTS-68 'F ...... 216.277130766009 A .............................. 0.000003371754 B .............................. 2.000000000000 Rho60* ......................... 820.656877671821 a l ha60 ........................ 0.000490440878 de?ta t. 'F .................... 156.270255866009 C t l " ........................... 0.921879416463 Fp, ps i ......................... 0.960919556350 P i n ps i ....................... 508.357292359977 cp l ............................ 1.004908884069 Ctpl* .......................... 0.926404815644 Density a t t & P . kg/cu m ...... 760.257920070010

Correct ing 60'F densi ty t o 1 5 ' C base conditions: t. F .......................... 59.000000000000 t corrected t o IPTS-68 'F ...... 59.006621316269 A .............................. 0.000003371754 B .............................. 2.000000000000 Rho60* ......................... 820.656877671821 a l ha60 ........................ 0.000490440878 de?ta t . O F .................... -1.000253583731 C t l ............................ 1.000490495623 Fp. ps i ......................... 0.546539446476 P i n ps i ....................... 0.000000000000 cp1 ............................ 1.000000000000 Ctpl ........................... 1.000490495623

step 4



--`,,`,,,-`-`,,`,,`,`,,`---


Density, kg/cu m, a t i S ' C / O kpa 821.056637883991 Ct1,60 ......................... 1.000490495623


C t 1 , O ..................... C t l ....................... C t D l . 0 ....................

culate the Ctpl f ac to r f o r 1 5 ' C base condit ions: . . . . 0.993590934183 . . . . 0.921427460327 .... 0.995729115724

Fp-,o, kpa . . . . . . . . . . Fp,kPa ............

volume a t base cond volume a t a l te rna te

step 6

.... 0.99573 c t p l ;o, rounded . . . . . . . . . . . ~ ~ ~ ~

Ctpl . . . . . . . . . . . . . . . . . . . . . . . . . . Ctpl , rounded ..... ............ 0.92595

Ö.925950640907

............ 0.083069734480

............ 0.139369604520

t i ons ...... 9944.853375000 condit ions . 10740.162400778



--`,,`,,,-`-`,,`,,`,`,,`---


Example 5

Commodi t y ...................... General i zed Refined Product t observed. 'C ................. 1.85

1835 Base temperature. c ........... 20 t a l ternate temp. 'C ........... 45.95 P a l ternate pressure. kpa ...... 10342 Observed densi ty. kg/cu m ...... 799 volume a t observed t & P ....... 15.85

Inpu t Data




T base. F ..................... 68 t observed. 'F ................. 35.33 t a l ternate temperature. 'F .... 114.71 P observed pressure. PSI ....... 266.144260052 P a l ternate pressure. PSI ...... 1499.98034739

Correct ing observed densi ty t o 60'F & O ps i reference condi t ions step 2

I terat ion(m) ..... 0 1 2 3 Commodity .......... j e t f ue l t rans i t i on t rans i t i on t rans i t i on

Kû(m) .............. 330.301000000000 1.48906700000e+03 1.48906700000e+03 1.48906700000e+03 Kï(m) 0.000000000000 0.000000000000 0.000000000000 0.000000000000

A(m) ............... 0.000003556989 0.000003662297 0.000003662535 0.000003662537 B(M) ............... 2.000000000000 9.01475 5727047 9.014299762272 9.014296341125 Rho60*(m) .......... 799.002842027463 787.504556505496 787.498878091552 787.498835483549 a l ha60(m) ......... 0.000517384293 0.000532688062 0.000532722689 0.000532722949

Fp(m) .............. 0.539219872095 0.561431824168 0.561443262359 O . 561443348187

Rho60(m) ........... 799.000000000000 787.501672522079 787.495993941460 787.495951332206

..............

.............. Kï(m) 0.000000000000 -0.001868400000 -0.001868400000 -0.001868400000

C t ? 60(m) .......... 1.012716874189 1.013091459604 1.013092307056 1.013092313415 ......... d-ai pha(m) 2.000000000000 8.500000000000 8.500000000000 8.500000000000

Cpl (m) 1.001437165218 1.001496454604 1.001496485138 1.001496485367 Ctpl(m) 1.014172315657 1.014607504983 1.014608384637 1.014608391238 Rho60(m)xctpl. 60(m) 810.323680209578 799.005107127664 799.000038321080 799.000000287288 de l ta ~ho6O(m) ..... -11.323680209578 -0.005107127664 -0.000038321080 -0.000000287288 E(M) ............... -11.165440068483 -0.005033599337 -0.000037769331 Dt(m) .............. -0.025006408584 -0.109353347057 -0.109360302838 Dp(m) .............. -0.003944533201 -0.004228078613 -0.004228225860 de l ta Rho(m) ....... -11.498327477921 -0.005678580620 -0.000042609254 Rho60(m+l) ......... 787.501672522079 787.495993941460 787.495951332206

............. ............

Output values Rho60 .......................... 787.495951332206 C t l . o .......................... 1.013092313415 Fp.0. ps i ....................... 0.561443348187 Cpl. o .......................... 1.001496485367 Ctp l . o ......................... 1.014608391238

step 3 Correct ing 60'F and O ps i densi ty t o a l ternate condi t ions:

t. F .......................... 114.710000000000 t corrected t o IPTS-68 'F ...... 114.731286608945 A .............................. 0.000003662537 B .............................. 9.014296341125 Rh060" ......................... 787.498835483549 a l ha60 ........................ 0.000532722949 de?ta t. 'F .................... 54.724411708945 C t l " ........................... 0.970607576134 Fp. ps i ......................... 0.764313263012 P i n ps i ....................... 1.49998034739e+03 cp l ............................ 1.011597508944 Ctpl* .......................... 0.981864206179 Density a t t & P. kg/cu m ...... 773.214087124006

Correct ing 60' F densi ty t o 20'C base conditions: t. F .......................... 68.000000000000 t corrected t o IPTS-68 'F ...... 68.008921288340 A .............................. 0.000003662537

step 4

........... B .............................. 9.Ö14296341125 Rh060" ......................... 787.498835483549 a l ha60 ........................ 0.000532722949

8 . 002046388340 de?ta t, O F .................... C t l ............................ 0.995731698796 Fp. ps i ......................... 0.637442285063 P i n ps i ....................... 0.000000000000 cp1 ............................ 1.000000000000 Ctpl ........................... 0.995731698796



--`,,`,,,-`-`,,`,,`,`,,`---


Density. kg/cu m . a t 20'c/O kpa 784.134681415189 C t l . 60 ......................... 0.995731698796

Sfep 5 Modify C t l * factor and ca cu la te the Ctpl f a c t o r for 20'c base condit ions:

C t l . o ......................... 1.017435032590 C t l ........................... 0.974768180331 C t p l . o ........................ 1.018957609228 Ctp1.o. rounded ............... 1.01896 Ctpl ........................... 0.986073063021

Fp.0. kpa ....................... 0.081430476547 Fp. kPa ......................... 0.110854271298

volume a t base condit ions ...... 16.150516000 volume a t a l t e r n a t e condit ions . 16.378670885

C t p l . rounded .................. 0.98607

step 6



--`,,`,,,-`-`,,`,,`,`,,`---


Example 6

t observed. 'C ................. 5.45 1708

Base temperature. c ........... 1 5 t a l ternate temp. 'C ........... -44.95 P a l ternate pressure. kpa ...... 348 observed densi ty. kg/cu m ...... 779.6 volume a t observed t & P ....... 201.5





T base. F ..................... 59 t observed. 'F ................. 41.81

P observed pressure. PSI ....... 247.724466577 P a l ternate pressure. PSI ...... 50.4731348763

Correct ing observed densi ty t o 6 0 ' ~ & O ps i reference condi t ions

t a l ternate temperature. 'F .... -48.91

step 2

I terat ion(m) ..... O 1 2 3 Commodity .......... t rans i t i on gasoline gasoline gasoline ~ho6O(m) ........... 779.600000000000 769.382460404541 769.455200805984 769.455206492347 KO(m) .............. 1.48906700000e+03 192.457100000000 192.457100000000 192.457100000000 K1(M) .............. 0.000000000000 0.243800000000 0.243800000000 0.243800000000 K2(m) .............. -0.001868400000 0.000000000000 0.000000000000 0.000000000000 A(m) ............... 0.000003998615 0.000004413697 0.000004413068 0.000004413068 B(M) ............... 8.424754338437 1.506422681731 1.506399050765 1.506399048917 ~ho6O*(m) .......... 779.603117231299 769.385856222133 769.458596461004 769.458602147354 a l ha6Ò(m) ......... 0.000581605759 0.000641997502 0.000641906079 0.000641906072

d-alpha(m) ......... 8.500000000000 1.500000000000 1.500000000000 1.500000000000 Fp(m) .............. 0.592853161339 0.616555878641 0.616380416094 0.616380402381 cp1 (m) ............. 1.001470802414 1.001529696158 1.001529260164 1.001529260130

C t ? , 6O(m) .......... 1.010547763402 1.011638979603 1.011637328270 1.011637328141

C b i ( Í l l ) ............ 1.012034079492 1.013186479863 1.013184384936 1.013184384772 ~hbGÒ(m)xCtpl. 60(m) 788.981768372203 779.527906725858 779.599994364210 779.599999999553 de l ta ~ho6O(m) ..... -9.381768372203 0.072093274142 0.000005635790 0.000000000447 E(M) ............... -9.270209929007 0.071154990295 0.000005562452 Dt(m) .............. -0.088402809484 -0.017189603867 -0.017187202601 Dp(m) .............. -0.004313216483 -0.004605864910 -0.004603681605 de l ta Rho(m) ....... -10.217539595459 0.072740401443 0.000005686363 RhoGO(m+lj ........ 769.382460404541 769.455200805984 769.455206492347

Rho60 .......................... 769.455206492347 C t l , o .......................... 1.011637328141

cp l . o .......................... 1.001529260130 c t p l . o ......................... 1.013184384772

output values

Fp.0. ps i ....................... 0.616380402381


t. F .......................... -48.910000000000 t corrected t o IPTS-68 'F ...... -48.926020214553 A .............................. 0.000004413068 B .............................. 1.506399048917 Rho60* ......................... 769.458602147354 alpha60 ........................ 0.000641906072 d e i i a t. 'F .................... -108.932895114553 C t l ........................... 1.068241256966 Fp. ps i ......................... 0.426326280590 P i n ps i ....................... 50.473134876255 cp l ............................ 1.000215226551 Ctpl' .......................... 1.068471170847 Density a t t & P. kg/cu m ...... 822.140705395444

Steo 4 Corre;ting 6 0 ' ~ densi ty t o 1 5 ' C base condi t ions:

t. F .......................... 59.000000000000 t corrected t o IPTS-68 'F ...... 59.006621316269 A .............................. 0.000004413068 B .............................. 1.506399048917 Rho60* ......................... 769.458602147354 a l ha60 ........................ 0.000641906072 de?ta t , O F .................... -1.000253583731 C t l ............................ 1.000641949542 Fp, ps i ......................... 0.660979356291 P i n ps i ....................... 0.000000000000 cp1 ............................ 1.000000000000 Ctpl ........................... 1.000641949542



--`,,`,,,-`-`,,`,,`,`,,`---


Density, kg/cu m, a t i S ' C / O kpa 769.949157909619 Ct1,60 ......................... 1.000641949542

Sfep 5 Modify C t l * f a c t o r and ca

C t 1 , O ..................... C t l ....................... C t D l . 0 ....................

culate the Ctpl f a c t o r f o r 1 5 ' C base condi t ions: .... 1.010988324649 .... 1.067555939919 . . . . 1.012534388785

Ctpl ;o, rounded . . . . . . . . . . . . . . . 1.01253 Ctpl ...................... .... 1.067785706302 Ctp l , rounded ..... ............ 1.06779

............ 0.089398422944

............ 0.061833401901 Fp-,o, kpa . . . . . . . . . . Fp,kPa ............

volume a t base cond volume a t a l ternate

step 6 t i ons ...... 204.024795000 condi t ions . 191.072022589



--`,,`,,,-`-`,,`,,`,`,,`---


commod; t y ...................... 0.00057634

t observed, c ................. 29.2

Speci a l i zed L i qui d Alpha a t 6 0 ' ~ per 'F ........... P observed pressure, kpa ....... Base temperature, c ........... t a l te rna te temp, 'C ........... P a l te rna te pressure, kpa ...... observed density, kg/cu m ...... volume a t observed t & P .......

395 1 5

55.05 6505

853.7 1000



T base, F ..................... 59 t observed, 'F ................. 84.56 t a l te rna te temperature, 'F .... 131.09 P observed pressure, PSI ....... 57.2899088394 P a l ternate pressure, PSI ...... 943.470524052

Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions step 2

I terat ion(m) ..... O 1 2 ~ho6O(m) ........... 853.700000000000 865.756362250420 865.756106602179 Rho60G(m) .......... 853.703382614631 865.759792635963 865.759536986708 Ct l ,GO(m) .......... 0.985782987747 0.985782987747 0.985782987747 d-alpha(m) ......... 0.000000000000 0.000000000000 0.000000000000

...... 0.535748682507 0.515981715023 O. 515982117769

...... 1.000307024167 1.000295692863 1.000295693093

...... 0.986085646948 0.986074476741 0.986074476968

Fp(mj ........ cp l (m) ....... c t p l (m) ...... Rho60 (m) xc tp l del t a ~ho6O(m E(M) ........ Dt(m> .......

60(m) 841.821316799279 853.700251891176 853.700000000005 ..... 11.878683200722 -0.000251891176 -0.000000000004

...... 12.046299667265 -0.000255448429

...... 0.000000000000 0.000000000000

...... -0.000834628468 -0.000781592986

...... 12.056362250420 -0.000255648241

60(m) 841.821316799279 853.700251891176 853.700000000005 ..... 11.878683200722 -0.000251891176 -0.000000000004 ...... 12.04 29 ...... 0.oc 300000 ...... -0.oc 36 ...... 12.05 $1 ...... 865.756362250420 865.756106602179

Dpimj ....... de l ta Rho(m) ~hoGO(m+l) . . Rho60 .......................... 865.756106602179

cp1,o .......................... 1.000295693093 ctp1,o ......................... 0.986074476968

output valu -

C t 1 , O .......................... 0.985782987747 Fp,O,pSi ....................... 0.515982117769


t, F .......................... 131.090000000000 t corrected t o IPTS-68 'F ...... 131.115680255004 Rho60* ......................... 865.759536986708 a l ha60 ........................ 0.000576340000 de?ta t , O F .................... 71.108805355004 C t l * ........................... 0.958556488638 Fp,pSi ......................... 0.599894402634 P i n mi ....................... 943.470524051827 cp l ............................ 1.005692042841 Ctpl' .......................... 0.964012633237 Density a t t & P, kg/cu m ...... 834.599824066622


t, 'F ........... t corrected t o IP Rho60* .......... a l ha60 ......... de?ta t. ..... C t l ............. Fp,psi .......... P i n ps i ........ cp1 ............. ctp1 ............. Density , kg/cu m , Ctl ,60 ...........

density t o 1 5 ' C base condit ions:

5-68 'F ...... .............. .............. .............. .............. .............. .............. .............. .............. a t i S ' C / O kpa ..............

1.000576389985 0.474992948912

Sfep 5 Modify C t l * f ac to r and ca lcu la te the Ctpl f ac to r f o r 1 5 ' C base condit ions:

Ct1,o .......................... 0.985215119619 C t l ............................ 0.958004304551 ctp1,o ......................... 0.985506440926 c tp l ,o , rounded ................ 0.98551 Ctpl ........................... 0.963457306095



--`,,`,,,-`-`,,`,,`,`,,`---


C t p l . rounded .................. 0.96346 Fp.0. kpa ....................... 0.074836882253 Fp. kPa ......................... 0.087007330735

step 6 volume a t base condit ions ...... 985.510000000 vol Ume a t a l te rnate condi ti ons . 1022.886264090



--`,,`,,,-`-`,,`,,`,`,,`---


Example 8

t observed. 'C ................. -49.95

Base temperature. c ........... 1 5 t a l te rna te temp. 'C ........... 67.65 P a l ternate pressure. bar ...... 13.65 observed density. kg/cu m ...... 1204.65

Input Data Commodi t y ...................... General i 1 zed Lube O i

P observed pressure. bar ....... 3 1 . 1

volume a t observed t & P 200.04 ....... computed Data - l a s t d i g i t i s rounded f o r display purposes


T base. F ..................... 59 t observed. 'F ................. -57.91 t a l te rna te temperature. 'F .... 153.77 P observed pressure. PSI ....... 451.067383521 P a l ternate pressure. PSI ...... 197.97652042

Correcting observed density t o 6 0 ' ~ & O ps i reference condit ions Note. Rho60 has been l i m i t e d t o the maximum tab le value i n one o r more cases .

step 2

I terat ion(m) ..... O 1 2 ~ho6O(m) ........... 1.16350000000e+03 1.16279157433e+03 1.16279156929e+03 KO(m) .............. 0.000000000000 0.000000000000 0.000000000000 K1(M) .............. 0.348780000000 0.348780000000 0.348780000000 K2(m) .............. 0.000000000000 0.000000000000 0.000000000000 A(m) ............... 0.000002060874 O . 000002062130 O . 000002062130 B(M) ............... 1.000000000000 1.000000000000 RhO60" (m) .......... a l ha60(m) ......... d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~hoGO(m)xctpl. 60(m) del t a ~ho6O(m) ..... Dt(m) .............. DD(m) ..............

C t ? . 6O(m) .......... Fp(& ..............

E(M) ...............

+03

+O3

1.16279397216e 0.000299949955 1.034970997658 1.000000000000 0.219819089881 1.000992516329 1.035998223273 1.20465000504e

-0.000005041899 -0.000004866707 -0.033365768499 -0.000967821268

dk ì ta Rho(m) ....... -0.708425670699 -0.000005039739 ~hoGO(m+l) ......... 1.16279157433e+03 1.16279156929e+03

output values Rho60 ...........

1.000992516333 1.035998223427

03 ¡.2Ö465ÖÖÖÖOÖe+03 -0.000000000034

C t l .o ............ cp1 .o ........... ctp1 .o .......... Fp.0. ps i .........

............... 1.16279156929e+03 .............. 1.034970997807 .............. 0.219819090810


t corrected t o IP

Rho60* ........... a l ha60 ..........

t. F ........... A ............... B ...............

de?ta t . ......

.............. 1.000992516333

.............. 1.035998223427

and O ps i density t o a l te rna te condit ions: .............. 153.770000000000 5-68 'F ...... 153.801698849288 .... _ ~ _ _ .............. 0.000002062130 .............. 1.000000000000 .............. 1.16279396712e+03 .............. 0.000299949957 .............. 93.794823949288

C t l * ........................... 0.971642779704 Fp. ps i ......................... 0.325535400898 P i n ps i ....................... 197.976520419791 CD1 ............................ 1.000644899286 c t p l * .......................... 0 . 972269391439 Density a t t & P. kg/cu m ...... 1.13054665144e+03

Correcting 6 0 ' ~ density t o 1 5 ' C base condit ions: t. F .......................... 59.000000000000 t corrected t o IPTS-68 'F ...... 59.006621316269 A .............................. 0.000002062130 B .............................. ~.oooooooooooo Rho60* ......................... 1.16279396712e+03 alpha60 ........................ 0.000299949957 de l ta t. 'F .................... -1.000253583731 C t l ............................ 1.000299999987 Fp. ps i ......................... 0.273053327335 P i n ps i ....................... 0.000000000000 cp1 ............................ 1.000000000000

step 4



--`,,`,,,-`-`,,`,,`,`,,`---


Ctpl ........................... 1.000299999987 Density. kg/cu m. a t 15'C/O bar 1163.140406745777 C t l . 60 ......................... 1.000299999987

step 5 Modify C t l * f ac to r and ca

C t l . o ..................... C t l ....................... ctp1. o .................... c t p l .o. rounded ........... ctp1 ...................... c t p l . rounded .............. Fp.0. bar ................... Fp. bar .....................

culate the Ctpl f ac to r f o r 1 5 ' C base condit ions: .... 1.034660599640 .... 0.971351374304 .... 1.035687517185 .... 1.03569 .... 0.971977798112 .... 0.97198 .... 3.188206499661 .... 4.721492010499

step 6 volume a t base condit ions ...... 207.179427600 volume a t a l te rna te condit ions . 213.151945102



--`,,`,,,-`-`,,`,,`,`,,`---


Example 9

t observed, ?C ................. 35.8 140

Base temperature, c ........... 20 t a l te rna te temp, ?C ........... 150 P a l te rna te pressure, kpa ...... 10340 observed density, kg/cu m ...... 734.29 volume a t observed t & P ....... 12501

Input Data Commodi t y ...................... General i zed Lube O i 1

P observed pressure, kpa .......


s tep 1 Convert t o customary u n i t s

T base, F ..................... 68 t observed, ? F ................. 96.44 t a l te rna te temperature, ? F .... 302 P observed pressure, PSI ....... 20.3052841456 P a l ternate pressure, PSI ...... 1499.6902719

step 2 Correcting observed densi ty t o 6 0 ? ~ & O ps i reference condit ions Note, Rho60 has been l i m i t e d t o the minimum t a b l e value i n one o r more cases.

I terat ion(m) ..... O 1 2 Rho6O(m) ........... KO(m) .............. K1(M) .............. K2(m) .............. A(m) ............... B(M) ............... ~ho6O*(m) .......... a l ha60(m) ......... d-al ha(m) ......... cp l (m) ............. c t p l (m) ............ ~ho6O(m)xctpl, 60(m) d e l t a ~ho6O(m) . .

Ct?,6O(m) .......... Fp(& ..............

E(M) ............ Dp(m) ........... Dt(m) ........... d e l t a Rho(m) .... ~ho6O(m+l) ......

convergence no t Density i s outs

..

..

..

..

..

.. ach de

?8ÓO. 900000000000 800.900000000000 800.900000000000 ............. .............. ..............

o. ööoooooooooo o. öooooooooooo o. öooooooooooo 0.348780000000 0.348780000000 0.348780000000 0.000000000000 0.000000000000 0.000000000000 0.000002993915 0.000002993915 0.000002993915 1.000000000000 1.000000000000 1.000000000000

800.902397828986 800.902397828986 800.902397828986

1.000136910811 1.000136910811 1.000136910811 0.984188421635 0.984188421635 0.984188421635

788.236506887413 788.236506887413 788.236506887413 -53.946506887413 -53.946506887413 -53.946506887413 -54.813189935518 -54.813189935518 -54.813189935518

0.016271950498 0.016271950498 0.016271950498 -0.000434671401 -0.000434671401 -0.000434671401 0.000000000000 0.000000000000 0.000000000000

800.900000000000 800.900000000000 800.900000000000

eved a f t e r 1 5 i t e r a t i o n s , so lu t ion no t found. i m i t s o f procedure

... 14

... 800.900000000000

... 0.000000000000

... 0.348780000000

... 0.000000000000

... 0.000002993915

... 1.000000000000

...

...

...

...

...

...

...

...

...

...

...

...

800.902397828986 0.000435483775 0.984053694045 1.000000000000 0.674169679903 1.000136910811 0.984188421635

... 0.000000000000

... 800.900000000000



--`,,`,,,-`-`,,`,,`,`,,`---


Example 10

t observed, 'C ................. -50.05 O

Base temperature, c ........... 1 5 t a l te rna te temp, 'C ........... -50.05 P a l te rna te pressure, kpa ...... O observed density, kg/cu m ...... 470.27 volume a t observed t & P ....... 1000

Inpu t Data Commodity ...................... Generalized crude O i l




T base, F ..................... 59 t observed, 'F ................. -58.09 t a l te rna te temperature, 'F .... -58.09 P observed pressure, PSI ....... O P a l te rna te pressure, PSI ...... O observed temperature less than -5O'C ( -58 '~ ) - outside l i m i t s o f t a b l e Al ternate temperature less than -5O'C ( -58 '~ ) - outside l i m i t s o f t a b l e Density less than 470.4 kg/cu m - outside l i m i t s o f tab le

Example 11

t observed, 'C ................. 150.03 103.425

Base temperature, c ........... 1 5 t a l te rna te temp, 'C ........... 150.03 P a l ternate pressure, bar ...... 103.425 observed density, kg/cu m ...... 1201.85 volume a t observed t & P ....... 1000

Inpu t Data Commodity ...................... Generalized crude O i l

P observed pressure, bar .......



T base, F ..................... 59 t observed, 'F ................. 302.054 t a l te rna te temperature, 'F .... 302.054 P observed pressure, PSI ....... 1500.05286626 P a l ternate pressure, PSI ...... 1500.05286626 observed temperature greater than 150'C (302 '~) - outside l i m i t s o f tab le Al ternate temperature greater than 150'C (302 '~) - outside l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o f tab le Al ternate pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1201.8 kg/cu m - outside l i m i t s o f t a b l e



--`,,`,,,-`-`,,`,,`,`,,`---


Example 12

t observed, 'C ................. 150.02 10342.5

Base temperature, c ........... 1 5 t a l te rna te temp, 'C ........... 150.02 P a l te rna te pressure, kpa ...... 10342.5 observed density, kg/cu m ...... 1209.56 volume a t observed t & P ....... 1000





T base, F ..................... 59 t observed, 'F ................. 302.036 t a l te rna te temperature, 'F .... 302.036 P observed pressure, PSI ....... 1500.05286626 P a l ternate pressure, PSI ...... 1500.05286626 observed temperature greater than 150'C (302 '~) - outside i m i t s o f tab le Al ternate temperature greater than 150.C (302 '~) - oufside l i m i t s o f tab le observed pressure greater than 1500 ps i - outside l i m i t s o tab le Al ternate pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1209.5 kg/cu m - outside l i m i t s o f t a b l e

Example 13

t observed, 'C ................. 25.56 10342.5

Base temperature, c ........... 1 5 t a l te rna te temp, 'C ........... 36.85 P a l te rna te pressure, kpa ...... O observed density, kg/cu m ...... 1208.52 volume a t observed t & P ....... 1000

Inpu t Data Commodi t y ...................... General i zed Lube O i 1




T base, F ..................... 59 t observed, 'F ................. 78.008 t a l te rna te temperature, 'F .... 98.33 P observed pressure, PSI ....... 1500.05286626 P a l te rna te pressure, PSI ...... O observed pressure greater than 1500 ps i - outside l i m i t s o f tab le Density greater than 1208.3 kg/cu m - outside l i m i t s o f tab1



--`,,`,,,-`-`,,`,,`,`,,`---


Pressure Value & Units

11.1.8 Use of Implementation Procedures to Generate Correction Factors in Tabular Format

Output & Units

This Standard incorporates both the temperature and pressure corrections into a single, unified procedure. Creating a full "three dimensional" table representation of the Standard with all possible values of temperature, pressure, and density would produce such a large number of results as to be unmanageable. Therefore, this Standard is intended to be used in its algorithmic form. However, this section provides procedures for generating correction factors in tabular format that can be printed for convenience. The format of these tables is that of the historical Petroleum Measurement Tables.

Correction of Observed Specific Gravity to Specific

Gravity 60/60"F

Previous versions of this Standard had separate tables for the temperature and pressure corrections. These can still be created as specific cases of the general procedure. The equivalent of 1980 temperature correction tables can be generated by setting the pressure to the base value (one atmosphere). The equivalent of the pressure correction tables can be generated by printing the compressibility factor at the base pressure.

The following table shows the tabular format of the temperature correction and compressibility factor tables for which generation instructions will be given. Any deviation from the set of units and pressure value will give a custom table that will not have an official designation.

23A, 23B

Petrole um Meas u re me nt Tab les

Correction of Volume to 60°F Against Specific

Gravity 60/60"F

Table Designations Table Description

24A, 24B, 24C

I 5Ay5B,5D API Gravity Correction to 60°F

Compressibility Factors for Hydrocarbons Related to API

Temperature Gravity and Metering

Correction of Volume to 60°F Against API Gravity at

60°F

1984 Ch. 11.2.1

Compressibility Factors for Hydrocarbons Related to

Density and Metering Temperature

1984 Ch. 11.2.1M

I 53A, 53B, 53D Correction of Observed Density to Density at 15°C

54A, 54B, 54C, 54D

Correction of Volume to 15°C Against Density at

15°C

Correction of Observed Density to Density at 20°C 59A, 59B, 59D

60A, 60B, 60C, 60D

Correction of Volume to 20°C Against Density at

20°C

Input Value Temperature Base I 60°F I 0bserved"API

I I I

Observed Relative Density

600F I BaseRelative Density

Observed

Base kg/m3 150C I

Base kg/m3 20"c I

Base "API I Base kg/m3

150C I I

O psig I BaseOAPI

I I CTL

O psig

Base Relative Density O psig

O psig CTL I O kPa (gauge)

O kPa (gauge)

FP (Psi-') O psig

FP (kPa-') O kPa (gauge)

I



--`,,`,,,-`-`,,`,,`,`,,`---


These table representations of this Standard’s algorithm are to be generated with rounded input and be represented with rounded output. The procedure to round the values is given in 1 1.1.5.4.

Unlike previous editions of the VCF tables there are no provisions to correct density measurements with a glass hydrometer. It is essential that only corrected hydrometer values be used in conjunction with these tables. Glass hydrometer values should be corrected consistent with directions from the hydrometer manufacturer and appropriate glass hydrometer standard. The odd-numbered 1980 Tables all included a hydrometer correction. Because of this, the odd-numbered tables generated by the algorithm in this Standard will not be identical to the corresponding odd- numbered 1980 Tables. Appendix A includes a discussion of the hydrometer corrections used in the 1980 CTL Tables.



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.1 Instructions to Generate Table 5A - API Gravity Correction to 60°F for Generalized Crude Oils

Input Variables: Observed M I gravity and temperature. Pressure set to O psig.

Output Variables: M I gravity at 60'F.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step 7:

Hold pressure value at O psig.

Increment observed M I gravity value by 0.1'MI in range of -13.4' to 168.9'MI. Ensure that the observed M I gravity value remains rounded consistent with instructions in 1 1.1.5.4.

Increment observed temperature by 0.1'F in range of -58.0" to 302.0'F. Ensure that the observed temperature value remains rounded consistent with instructions in 1 1.1.5.4.

Convert density units from M I gravity to kg/m3 using procedure in 1 1.1.5.1.

Determine the base density using procedure in 1 1.1.6.2 & specifjdng commodity group "A."

Convert the density units from kg/m3 back to M I gravity using procedure in 1 1.1.5.1. Round the value of this M I gravity consistent with instructions in 1 1.1.5.4.

Increment the value of the M I gravity or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of M I gravity and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


Table 5A. Correction of Observed API Gravity to API Gravity at 60'F (Crude Oils) If hydrometer used to determine density, apply glass correction before entering table

OF

1 3 5 . O 1 3 5 . 1 1 3 5 . 2 1 3 5 . 3 1 3 5 . 4

1 3 5 . 5 1 3 5 . 6 1 3 5 . 7 1 3 5 . 8 1 3 5 . 9

1 3 6 . 0 1 3 6 . 1 1 3 6 . 2 1 3 6 . 3 1 3 6 . 4

1 3 6 . 5 1 3 6 . 6 1 3 6 . 7 1 3 6 . 8 1 3 6 . 9

1 3 7 . 0 1 3 7 . 1 1 3 7 . 2 1 3 7 . 3 1 3 7 . 4

1 3 7 . 5 1 3 7 . 6 1 3 7 . 7 1 3 7 . 8 1 3 7 . 9

1 3 8 . O 1 3 8 . 1 1 3 8 . 2 1 3 8 . 3 1 3 8 . 4

1 3 8 . 5 1 3 8 . 6 1 3 8 . 7 1 3 8 . 8 1 3 8 . 9

1 3 9 . O 1 3 9 . 1 1 3 9 . 2 1 3 9 . 3 1 3 9 . 4

1 3 9 . 5 1 3 9 . 6 1 3 9 . 7 1 3 9 . 8 1 3 9 . 9

1 4 0 . O

65 .0

5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0

5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0 5 5 . 9

5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9

5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 8 5 5 . 8

5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8

5 5 . 8 5 5 . 8 55 .7 55 .7 55 .7

55 .7 55 .7 55 .7 55 .7 55 .7

55 .7 5 5 . 6 5 5 . 6 5 5 . 6 5 5 . 6

5 5 . 6 5 5 . 6 5 5 . 6 5 5 . 6 5 5 . 6

5 5 . 5 5 5 . 5 5 5 . 5 5 5 . 5 5 5 . 5

5 5 . 5

Observed Pressure is O psig

Observed API Gravity 6 5 . 1 65.2 6 5 . 3 65.4 6 5 . 5

Corresponding Density at 60'F & O psig, "API

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 0 5 6 . 0

5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0

5 6 . 0 5 6 . 0 5 5 . 9 5 5 . 9 5 5 . 9

5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9

5 5 . 9 5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8

5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8

55 .7 55 .7 55 .7 55 .7 55 .7

55 .7 55 .7 55 .7 55 .7 5 5 . 6

5 5 . 6 5 5 . 6 5 5 . 6 5 5 . 6 5 5 . 6

5 5 . 6

56 .2 56 .2 56 .2 56 .2 56 .2

56 .2 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0

5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0

5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9

5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 8

5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8

5 5 . 8 5 5 . 8 5 5 . 8 55 .7 55 .7

55 .7 55 .7 55 .7 55 .7 55 .7

55 .7

5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3

56 .2 56 .2 56 .2 56 .2 56 .2

56 .2 56 .2 56 .2 56 .2 5 6 . 1

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 0 5 6 . 0

5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0

5 6 . 0 5 6 . 0 5 6 . 0 5 5 . 9 5 5 . 9

5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9

5 5 . 9 5 5 . 9 5 5 . 8 5 5 . 8 5 5 . 8

5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8 5 5 . 8

5 5 . 8

56 .4 56 .4 56 .4 56 .4 5 6 . 3

5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3

5 6 . 3 5 6 . 3 5 6 . 3 56 .2 56 .2

56 .2 56 .2 56 .2 56 .2 56 .2

56 .2 56 .2 5 6 . 1 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0

5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0

5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9

5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 9 5 5 . 8

5 5 . 8

5 6 . 5 5 6 . 5 5 6 . 5 56 .4 56 .4

56 .4 56 .4 56 .4 56 .4 56 .4

56 .4 56 .4 5 6 . 3 5 6 . 3 5 6 . 3

5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3

5 6 . 3 56 .2 56 .2 56 .2 56 .2

56 .2 56 .2 56 .2 56 .2 56 .2

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 0

5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0 5 6 . 0

5 6 . 0 5 6 . 0 5 6 . 0 5 5 . 9 5 5 . 9

5 5 . 9

6 5 . 6

5 6 . 6 5 6 . 6 5 6 . 5 5 6 . 5 5 6 . 5

5 6 . 5 5 6 . 5 5 6 . 5 5 6 . 5 5 6 . 5

5 6 . 5 56 .4 56 .4 56 .4 56 .4

56 .4 56 .4 56 .4 56 .4 56 .4

5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3

5 6 . 3 5 6 . 3 5 6 . 3 5 6 . 3 56 .2

56 .2 56 .2 56 .2 56 .2 56 .2

56 .2 56 .2 56 .2 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1

5 6 . 1 5 6 . 1 5 6 . 0 5 6 . 0 5 6 . 0

5 6 . 0

OF

1 3 5 . O 1 3 5 . 1 1 3 5 . 2 1 3 5 . 3 1 3 5 . 4

1 3 5 . 5 1 3 5 . 6 1 3 5 . 7 1 3 5 . 8 1 3 5 . 9

1 3 6 . 0 1 3 6 . 1 1 3 6 . 2 1 3 6 . 3 1 3 6 . 4

1 3 6 . 5 1 3 6 . 6 1 3 6 . 7 1 3 6 . 8 1 3 6 . 9

1 3 7 . 0 1 3 7 . 1 1 3 7 . 2 1 3 7 . 3 1 3 7 . 4

1 3 7 . 5 1 3 7 . 6 1 3 7 . 7 1 3 7 . 8 1 3 7 . 9

1 3 8 . O 1 3 8 . 1 1 3 8 . 2 1 3 8 . 3 1 3 8 . 4

1 3 8 . 5 1 3 8 . 6 1 3 8 . 7 1 3 8 . 8 1 3 8 . 9

1 3 9 . O 1 3 9 . 1 1 3 9 . 2 1 3 9 . 3 1 3 9 . 4

1 3 9 . 5 1 3 9 . 6 1 3 9 . 7 1 3 9 . 8 1 3 9 . 9

1 4 0 . O



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.2 Instructions to Generate Table 5B - API Gravity Correction to 60°F for Generalized Products



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step 7:


Increment observed M I gravity value by 0.1'MI in range of -14.2' to 168.9'MI. Ensure that the observed M I gravity value remains rounded consistent with instructions in 1 1.1.5.4.



Determine the base density using procedure in 11.1.6.2 & specifjdng commodity group "B."





--`,,`,,,-`-`,,`,,`,`,,`---


Table 5B. Correction of Observed API Gravity to API Gravity at 60'F (Refined Products) If hydrometer used to determine density, apply glass correction before entering table

OF

135. O 135.1 135.2 135.3 135.4

135.5 135.6 135.7 135.8 135.9

136.0 136.1 136.2 136.3 136.4

136.5 136.6 136.7 136.8 136.9

137.0 137.1 137.2 137.3 137.4

137.5 137.6 137.7 137.8 137.9

138. O 138.1 138.2 138.3 138.4

138.5 138.6 138.7 138.8 138.9

139. O 139.1 139.2 139.3 139.4

139.5 139.6 139.7 139.8 139.9

140. O

65.0

55.2 55.2 55.2 55.1 55.1

55.1 55.1 55.1 55.1 55.1

55.1 55.0 55.0 55.0 55.0

55.0 55.0 55.0 55.0 54.9

54.9 54.9 54.9 54.9 54.9

54.9 54.9 54.8 54.8 54.8

54.8 54.8 54.8 54.8 54.8

54.7 54.7 54.7 54.7 54.7

54.7 54.7 54.7 54.7 54.6

54.6 54.6 54.6 54.6 54.6

54.6


Observed API Gravity 65.1 65.2 65.3 65.4 65.5


55.3 55.3 55.2 55.2 55.2

55.2 55.2 55.2 55.2 55.2

55.1 55.1 55.1 55.1 55.1

55.1 55.1 55.1 55.0 55.0

55.0 55.0 55.0 55.0 55.0

55.0 54.9 54.9 54.9 54.9

54.9 54.9 54.9 54.9 54.8

54.8 54.8 54.8 54.8 54.8

54.8 54.8 54.8 54.7 54.7

54.7 54.7 54.7 54.7 54.7

54.7

55.4 55.3 55.3 55.3 55.3

55.3 55.3 55.3 55.3 55.2

55.2 55.2 55.2 55.2 55.2

55.2 55.2 55.1 55.1 55.1

55.1 55.1 55.1 55.1 55.1

55.0 55.0 55.0 55.0 55.0

55.0 55.0 55.0 54.9 54.9

54.9 54.9 54.9 54.9 54.9

54.9 54.9 54.8 54.8 54.8

54.8 54.8 54.8 54.8 54.8

54.7

55.4 55.4 55.4 55.4 55.4

55.4 55.4 55.4 55.3 55.3

55.3 55.3 55.3 55.3 55.3

55.3 55.2 55.2 55.2 55.2

55.2 55.2 55.2 55.2 55.1

55.1 55.1 55.1 55.1 55.1

55.1 55.1 55.0 55.0 55.0

55.0 55.0 55.0 55.0 55.0

55.0 54.9 54.9 54.9 54.9

54.9 54.9 54.9 54.9 54.8

54.8

55.5 55.5 55.5 55.5 55.5

55.5 55.5 55.4 55.4 55.4

55.4 55.4 55.4 55.4 55.4

55.3 55.3 55.3 55.3 55.3

55.3 55.3 55.3 55.2 55.2

55.2 55.2 55.2 55.2 55.2

55.2 55.1 55.1 55.1 55.1

55.1 55.1 55.1 55.1 55.1

55.0 55.0 55.0 55.0 55.0

55.0 55.0 55.0 54.9 54.9

54.9

55.6 55.6 55.6 55.6 55.6

55.6 55.5 55.5 55.5 55.5

55.5 55.5 55.5 55.5 55.4

55.4 55.4 55.4 55.4 55.4

55.4 55.4 55.3 55.3 55.3

55.3 55.3 55.3 55.3 55.3

55.2 55.2 55.2 55.2 55.2

55.2 55.2 55.2 55.2 55.1

55.1 55.1 55.1 55.1 55.1

55.1 55.1 55.0 55.0 55.0

55.0

65.6

55.7 55.7 55.7 55.7 55.7

55.6 55.6 55.6 55.6 55.6

55.6 55.6 55.6 55.5 55.5

55.5 55.5 55.5 55.5 55.5

55.5 55.4 55.4 55.4 55.4

55.4 55.4 55.4 55.4 55.3

55.3 55.3 55.3 55.3 55.3

55.3 55.3 55.2 55.2 55.2

55.2 55.2 55.2 55.2 55.2

55.2 55.1 55.1 55.1 55.1

55.1

OF

135. O 135.1 135.2 135.3 135.4

135.5 135.6 135.7 135.8 135.9

136.0 136.1 136.2 136.3 136.4

136.5 136.6 136.7 136.8 136.9

137.0 137.1 137.2 137.3 137.4

137.5 137.6 137.7 137.8 137.9

138. O 138.1 138.2 138.3 138.4

138.5 138.6 138.7 138.8 138.9

139. O 139.1 139.2 139.3 139.4

139.5 139.6 139.7 139.8 139.9

140. O



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.3 Instructions to Generate Table 5D - API Gravity Correction to 60°F for Generalized Lubricating Oils



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step 7:


Increment observed M I gravity value by O. l'MI in range of -14.1' to 66.3'MI. Ensure that the observed M I gravity value remains rounded consistent with instructions in 1 1.1.5.4.



Determine the base density using procedure in 1 1.1.6.2 & specifjdng commodity group "D."





--`,,`,,,-`-`,,`,,`,`,,`---


Table 5D. Correction of Observed API Gravity to API Gravity at 60'F (Lube Oils) If hydrometer used to determine density, apply glass correction before entering table

OF

135. O 135.1 135.2 135.3 135.4

135.5 135.6 135.7 135.8 135.9

136.0 136.1 136.2 136.3 136.4

136.5 136.6 136.7 136.8 136.9

137.0 137.1 137.2 137.3 137.4

137.5 137.6 137.7 137.8 137.9

138. O 138.1 138.2 138.3 138.4

138.5 138.6 138.7 138.8 138.9

139. O 139.1 139.2 139.3 139.4

139.5 139.6 139.7 139.8 139.9

140. O

0.0

-3.1 -3.1 -3.2 -3.2 -3.2

-3.2 -3.2 -3.2 -3.2 -3.2

-3.2 -3.2 -3.2 -3.2 -3.2

-3.2 -3.2 -3.2 -3.2 -3.2

-3.2 -3.2 -3.2 -3.2 -3.2

-3.2 -3.3 -3.3 -3.3 -3.3

-3.3 -3.3 -3.3 -3.3 -3.3

-3.3 -3.3 -3.3 -3.3 -3.3

-3.3 -3.3 -3.3 -3.3 -3.3

-3.3 -3.3 -3.3 -3.3 -3.3

-3.4


Observed API Gravity 0.1 0.2 0.3 0.4 0.5


-3.1 -3.1 -3.1 -3.1 -3.1

-3.1 -3.1 -3.1 -3.1 -3.1

-3.1 -3.1 -3.1 -3.1 -3.1

-3.1 -3.1 -3.1 -3.1 -3.1

-3.1 -3.1 -3.1 -3.1 -3.1

-3.2 -3.2 -3.2 -3.2 -3.2

-3.2 -3.2 -3.2 -3.2 -3.2

-3.2 -3.2 -3.2 -3.2 -3.2

-3.2 -3.2 -3.2 -3.2 -3.2

-3.2 -3.2 -3.2 -3.2 -3.3

-3.3

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0 -3.0 -3.0 -3.0 -3.1

-3.1 -3.1 -3.1 -3.1 -3.1

-3.1 -3.1 -3.1 -3.1 -3.1

-3.1 -3.1 -3.1 -3.1 -3.1

-3.1 -3.1 -3.1 -3.1 -3.1

-3.1 -3.1 -3.1 -3.2 -3.2

-3.2

-2.9 -2.9 -2.9 -2.9 -2.9

-2.9 -2.9 -2.9 -2.9 -2.9

-2.9 -2.9 -2.9 -2.9 -2.9

-2.9 -2.9 -2.9 -2.9 -2.9

-2.9 -2.9 -3.0 -3.0 -3.0

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0 -3.0 -3.1 -3.1 -3.1

-3.1

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8 -2.9 -2.9 -2.9 -2.9

-2.9 -2.9 -2.9 -2.9 -2.9

-2.9 -2.9 -2.9 -2.9 -2.9

-2.9 -2.9 -2.9 -2.9 -2.9

-2.9 -2.9 -2.9 -2.9 -2.9

-3.0 -3.0 -3.0 -3.0 -3.0

-3.0

-2.7 -2.7 -2.7 -2.7 -2.7

-2.7 -2.7 -2.7 -2.7 -2.7

-2.7 -2.7 -2.7 -2.7 -2.7

-2.7 -2.7 -2.7 -2.7 -2.7

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8 -2.8 -2.8 -2.8 -2.9

-2.9 -2.9 -2.9 -2.9 -2.9

-2.9

0.6

-2.6 -2.6 -2.6 -2.6 -2.6

-2.6 -2.6 -2.6 -2.6 -2.6

-2.6 -2.6 -2.6 -2.6 -2.6

-2.6 -2.6 -2.6 -2.6 -2.7

-2.7 -2.7 -2.7 -2.7 -2.7

-2.7 -2.7 -2.7 -2.7 -2.7

-2.7 -2.7 -2.7 -2.7 -2.7

-2.7 -2.7 -2.7 -2.7 -2.7

-2.7 -2.7 -2.7 -2.8 -2.8

-2.8 -2.8 -2.8 -2.8 -2.8

-2.8

OF

135. O 135.1 135.2 135.3 135.4

135.5 135.6 135.7 135.8 135.9

136.0 136.1 136.2 136.3 136.4

136.5 136.6 136.7 136.8 136.9

137.0 137.1 137.2 137.3 137.4

137.5 137.6 137.7 137.8 137.9

138. O 138.1 138.2 138.3 138.4

138.5 138.6 138.7 138.8 138.9

139. O 139.1 139.2 139.3 139.4

139.5 139.6 139.7 139.8 139.9

140. O



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.4 Instructions to Generate Tables 6A and 6B - Correction of Volume to 60°F Against API Gravity at 60°F for Generalized Crude Oils and Products

Input Variables: Base API gravity and temperature. Pressure set to O psig.

Output Variables: CTL at input temperature.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:


Increment base API gravity value by 0.1'API in range of -10.0" to 100.O'API. Ensure that the base API gravity value remains rounded consistent with instructions in 1 1.1.5.4.

Increment temperature by 0.1'F in range of -58.0' to 302.O'F. Ensure that the temperature value remains rounded consistent with instructions in 1 1.1.5.4.

Convert density units from API gravity to kg/m3 using procedure in 1 1.1.5.1.

Determine the CTL value using procedure in 11.1.6.1 & specifjdng commodity group "A" or "B" as appropriate. Round the CTL value consistent with instructions in 1 1.1.5.4.

Increment the value of the API gravity or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of API gravity and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


Table 6A. Volume Correction Factor Due to Temperature Against API Gravity at 60'F (Crude Oils)

OF

1 2 0 . o 1 2 0 . 1 1 2 0 . 2 1 2 0 . 3 1 2 0 . 4

1 2 0 . 5 1 2 0 . 6 1 2 0 . 7 1 2 0 . 8 1 2 0 . 9

1 2 1 . 0 1 2 1 . 1 1 2 1 . 2 1 2 1 . 3 1 2 1 . 4

1 2 1 . 5 1 2 1 . 6 1 2 1 . 7 1 2 1 . 8 1 2 1 . 9

1 2 2 . o 1 2 2 . 1 1 2 2 . 2 1 2 2 . 3 1 2 2 . 4

1 2 2 . 5 1 2 2 . 6 1 2 2 . 7 1 2 2 . 8 1 2 2 . 9

1 2 3 . O 1 2 3 . 1 1 2 3 . 2 1 2 3 . 3 1 2 3 . 4

1 2 3 . 5 1 2 3 . 6 1 2 3 . 7 1 2 3 . 8 1 2 3 . 9

1 2 4 . 0 1 2 4 . 1 1 2 4 . 2 1 2 4 . 3 1 2 4 . 4

1 2 4 . 5 1 2 4 . 6 1 2 4 . 7 1 2 4 . 8 1 2 4 . 9

1 2 5 . O

Alternate Pressure is O psig

Base API Gravity 95 .0 9 5 . 1 95 .2 95 .3 95 .4 95 .5 9 5 . 6

Volume Correction for the Effect of Temperature on Liquid (CTL) to 60'F

0 . 9 4 6 7 1 0 . 9 4 6 6 2 O . 9 4 6 5 3 0 . 9 4 6 4 4 O . 9 4 6 3 5

0 . 9 4 6 2 6 0 . 9 4 6 1 7 O . 9 4 6 0 8 0 . 9 4 5 9 9 O . 9 4 5 9 0

O . 9 4 5 8 1 O . 9 4 5 7 2 O . 9 4 5 6 3 O . 9 4 5 5 4 O . 9 4 5 4 5

O . 9 4 5 3 6 O . 9 4 5 2 7 O . 9 4 5 1 8 O . 9 4 5 0 9 O . 9 4 5 0 0

0 . 9 4 4 9 1 O . 9 4 4 8 2 0 . 9 4 4 7 3 0 . 9 4 4 6 4 O . 9 4 4 5 5

0 . 9 4 4 4 6 O . 9 4 4 3 7 O . 9 4 4 2 8 0 . 9 4 4 1 9 0 . 9 4 4 1 0

O . 9 4 4 0 1 O . 9 4 3 9 2 O . 9 4 3 8 3 O . 9 4 3 7 4 O . 9 4 3 6 5

O . 9 4 3 5 6 O . 9 4 3 4 7 O . 9 4 3 3 8 0 . 9 4 3 2 9 O . 9 4 3 2 0

O . 9 4 3 1 1 O . 9 4 3 0 2 O . 9 4 2 9 3 O . 9 4 2 8 4 O . 9 4 2 7 5

O . 9 4 2 6 6 O . 9 4 2 5 7 O . 9 4 2 4 8 O . 9 4 2 3 9 O . 9 4 2 3 0

O . 9 4 2 2 1

O . 9 4 6 6 6 O . 9 4 6 5 7 0 . 9 4 6 4 8 0 . 9 4 6 3 9 O . 9 4 6 3 0

0 . 9 4 6 2 1 O . 9 4 6 1 2 O . 9 4 6 0 3 O . 9 4 5 9 4 O . 9 4 5 8 5

0 . 9 4 5 7 6 O . 9 4 5 6 7 O . 9 4 5 5 8 0 . 9 4 5 4 9 O . 9 4 5 4 0

O . 9 4 5 3 1 O . 9 4 5 2 2 O . 9 4 5 1 3 O . 9 4 5 0 4 0 . 9 4 4 9 5

0 . 9 4 4 8 6 0 . 9 4 4 7 7 0 . 9 4 4 6 8 0 . 9 4 4 5 9 O . 9 4 4 5 0

0 . 9 4 4 4 1 O . 9 4 4 3 2 O . 9 4 4 2 3 0 . 9 4 4 1 4 O . 9 4 4 0 5

0 . 9 4 3 9 6 O . 9 4 3 8 7 O . 9 4 3 7 8 O . 9 4 3 6 9 O . 9 4 3 6 0

O . 9 4 3 5 1 O . 9 4 3 4 2 O . 9 4 3 3 3 O . 9 4 3 2 4 O . 9 4 3 1 5

O . 9 4 3 0 6 O . 9 4 2 9 7 O . 9 4 2 8 8 0 . 9 4 2 7 9 O . 9 4 2 7 0

O . 9 4 2 6 1 O . 9 4 2 5 2 O . 9 4 2 4 3 O . 9 4 2 3 4 O . 9 4 2 2 5

0 . 9 4 2 1 6

O . 9 4 6 6 1 O . 9 4 6 5 2 0 . 9 4 6 4 3 O . 9 4 6 3 4 0 . 9 4 6 2 5

0 . 9 4 6 1 6 O . 9 4 6 0 7 O . 9 4 5 9 8 O . 9 4 5 8 9 O . 9 4 5 8 0

O . 9 4 5 7 1 O . 9 4 5 6 2 O . 9 4 5 5 3 O . 9 4 5 4 4 O . 9 4 5 3 5

0 . 9 4 5 2 6 O . 9 4 5 1 7 O . 9 4 5 0 8 0 . 9 4 4 9 9 0 . 9 4 4 9 0

O . 9 4 4 8 1 O . 9 4 4 7 2 0 . 9 4 4 6 3 O . 9 4 4 5 4 0 . 9 4 4 4 5

0 . 9 4 4 3 6 O . 9 4 4 2 7 0 . 9 4 4 1 8 0 . 9 4 4 0 9 O . 9 4 4 0 0

O . 9 4 3 9 1 O . 9 4 3 8 2 O . 9 4 3 7 3 O . 9 4 3 6 4 O . 9 4 3 5 5

0 . 9 4 3 4 6 O . 9 4 3 3 7 O . 9 4 3 2 8 0 . 9 4 3 1 9 O . 9 4 3 1 0

O . 9 4 3 0 1 O . 9 4 2 9 2 O . 9 4 2 8 3 O . 9 4 2 7 4 O . 9 4 2 6 5

O . 9 4 2 5 6 O . 9 4 2 4 7 O . 9 4 2 3 8 O . 9 4 2 2 9 O . 9 4 2 2 0

O . 9 4 2 1 1

0 . 9 4 6 5 6 0 . 9 4 6 4 7 O . 9 4 6 3 8 0 . 9 4 6 2 9 0 . 9 4 6 2 0

0 . 9 4 6 1 1 O . 9 4 6 0 2 O . 9 4 5 9 3 O . 9 4 5 8 4 O . 9 4 5 7 5

O . 9 4 5 6 6 O . 9 4 5 5 7 O . 9 4 5 4 8 O . 9 4 5 3 9 O . 9 4 5 3 0

O . 9 4 5 2 1 O . 9 4 5 1 2 O . 9 4 5 0 3 0 . 9 4 4 9 4 O . 9 4 4 8 5

0 . 9 4 4 7 6 0 . 9 4 4 6 7 O . 9 4 4 5 8 0 . 9 4 4 4 9 0 . 9 4 4 4 0

O . 9 4 4 3 1 O . 9 4 4 2 2 0 . 9 4 4 1 3 O . 9 4 4 0 4 O . 9 4 3 9 5

O . 9 4 3 8 6 O . 9 4 3 7 7 O . 9 4 3 6 8 O . 9 4 3 5 9 O . 9 4 3 5 0

O . 9 4 3 4 1 O . 9 4 3 3 2 O . 9 4 3 2 3 O . 9 4 3 1 4 O . 9 4 3 0 5

0 . 9 4 2 9 6 O . 9 4 2 8 7 O . 9 4 2 7 8 O . 9 4 2 6 9 O . 9 4 2 6 0

O . 9 4 2 5 0 O . 9 4 2 4 1 O . 9 4 2 3 2 O . 9 4 2 2 3 O . 9 4 2 1 4

O . 9 4 2 0 5

O . 9 4 6 5 2 0 . 9 4 6 4 3 O . 9 4 6 3 4 0 . 9 4 6 2 5 0 . 9 4 6 1 6

O . 9 4 6 0 7 O . 9 4 5 9 8 O . 9 4 5 8 8 0 . 9 4 5 7 9 O . 9 4 5 7 0

O . 9 4 5 6 1 O . 9 4 5 5 2 O . 9 4 5 4 3 O . 9 4 5 3 4 O . 9 4 5 2 5

0 . 9 4 5 1 6 O . 9 4 5 0 7 0 . 9 4 4 9 8 0 . 9 4 4 8 9 O . 9 4 4 8 0

0 . 9 4 4 7 1 0 . 9 4 4 6 2 O . 9 4 4 5 3 0 . 9 4 4 4 4 O . 9 4 4 3 5

0 . 9 4 4 2 6 0 . 9 4 4 1 7 O . 9 4 4 0 8 0 . 9 4 3 9 9 O . 9 4 3 9 0

O . 9 4 3 8 1 O . 9 4 3 7 2 O . 9 4 3 6 3 O . 9 4 3 5 4 O . 9 4 3 4 5

O . 9 4 3 3 6 O . 9 4 3 2 7 O . 9 4 3 1 8 O . 9 4 3 0 9 O . 9 4 3 0 0

O . 9 4 2 9 1 O . 9 4 2 8 1 O . 9 4 2 7 2 O . 9 4 2 6 3 O . 9 4 2 5 4

O . 9 4 2 4 5 O . 9 4 2 3 6 O . 9 4 2 2 7 O . 9 4 2 1 8 O . 9 4 2 0 9

O . 9 4 2 0 0

0 . 9 4 6 4 7 O . 9 4 6 3 8 0 . 9 4 6 2 9 0 . 9 4 6 2 0 0 . 9 4 6 1 1

O . 9 4 6 0 2 O . 9 4 5 9 3 O . 9 4 5 8 4 O . 9 4 5 7 5 O . 9 4 5 6 6

O . 9 4 5 5 7 O . 9 4 5 4 8 O . 9 4 5 3 9 0 . 9 4 5 2 9 O . 9 4 5 2 0

O . 9 4 5 1 1 O . 9 4 5 0 2 0 . 9 4 4 9 3 O . 9 4 4 8 4 0 . 9 4 4 7 5

0 . 9 4 4 6 6 O . 9 4 4 5 7 0 . 9 4 4 4 8 0 . 9 4 4 3 9 O . 9 4 4 3 0

O . 9 4 4 2 1 O . 9 4 4 1 2 O . 9 4 4 0 3 O . 9 4 3 9 4 O . 9 4 3 8 5

0 . 9 4 3 7 6 O . 9 4 3 6 7 O . 9 4 3 5 8 0 . 9 4 3 4 9 O . 9 4 3 4 0

O . 9 4 3 3 1 O . 9 4 3 2 2 O . 9 4 3 1 3 O . 9 4 3 0 4 O . 9 4 2 9 4

O . 9 4 2 8 5 0 . 9 4 2 7 6 O . 9 4 2 6 7 O . 9 4 2 5 8 0 . 9 4 2 4 9

O . 9 4 2 4 0 O . 9 4 2 3 1 O . 9 4 2 2 2 O . 9 4 2 1 3 O . 9 4 2 0 4

0 . 9 4 1 9 5

O . 9 4 6 4 2 O . 9 4 6 3 3 0 . 9 4 6 2 4 0 . 9 4 6 1 5 0 . 9 4 6 0 6

O . 9 4 5 9 7 O . 9 4 5 8 8 0 . 9 4 5 7 9 O . 9 4 5 7 0 O . 9 4 5 6 1

O . 9 4 5 5 2 O . 9 4 5 4 3 O . 9 4 5 3 4 O . 9 4 5 2 5 0 . 9 4 5 1 6

O . 9 4 5 0 7 0 . 9 4 4 9 7 O . 9 4 4 8 8 0 . 9 4 4 7 9 0 . 9 4 4 7 0

0 . 9 4 4 6 1 O . 9 4 4 5 2 0 . 9 4 4 4 3 O . 9 4 4 3 4 O . 9 4 4 2 5

0 . 9 4 4 1 6 O . 9 4 4 0 7 O . 9 4 3 9 8 O . 9 4 3 8 9 O . 9 4 3 8 0

O . 9 4 3 7 1 O . 9 4 3 6 2 O . 9 4 3 5 3 O . 9 4 3 4 4 O . 9 4 3 3 5

0 . 9 4 3 2 6 O . 9 4 3 1 7 O . 9 4 3 0 7 O . 9 4 2 9 8 O . 9 4 2 8 9

O . 9 4 2 8 0 O . 9 4 2 7 1 0 . 9 4 2 6 2 O . 9 4 2 5 3 O . 9 4 2 4 4

O . 9 4 2 3 5 O . 9 4 2 2 6 O . 9 4 2 1 7 O . 9 4 2 0 8 0 . 9 4 1 9 9

0 . 9 4 1 9 0

1 2 0 . o 1 2 0 . 1 1 2 0 . 2 1 2 0 . 3 1 2 0 . 4

1 2 0 . 5 1 2 0 . 6 1 2 0 . 7 1 2 0 . 8 1 2 0 . 9

1 2 1 . 0 1 2 1 . 1 1 2 1 . 2 1 2 1 . 3 1 2 1 . 4

1 2 1 . 5 1 2 1 . 6 1 2 1 . 7 1 2 1 . 8 1 2 1 . 9

1 2 2 . o 1 2 2 . 1 1 2 2 . 2 1 2 2 . 3 1 2 2 . 4

1 2 2 . 5 1 2 2 . 6 1 2 2 . 7 1 2 2 . 8 1 2 2 . 9

1 2 3 . O 1 2 3 . 1 1 2 3 . 2 1 2 3 . 3 1 2 3 . 4

1 2 3 . 5 1 2 3 . 6 1 2 3 . 7 1 2 3 . 8 1 2 3 . 9

1 2 4 . 0 1 2 4 . 1 1 2 4 . 2 1 2 4 . 3 1 2 4 . 4

1 2 4 . 5 1 2 4 . 6 1 2 4 . 7 1 2 4 . 8 1 2 4 . 9

1 2 5 . O



--`,,`,,,-`-`,,`,,`,`,,`---


Table 6B. Volume Correction Factor Due to Temperature Against API Gravity at 60'F

OF

120. o 120.1 120.2 120.3 120.4

120.5 120.6 120.7 120.8 120.9

121.0 121.1 121.2 121.3 121.4

121.5 121.6 121.7 121.8 121.9

122. o 122.1 122.2 122.3 122.4

122.5 122.6 122.7 122.8 122.9

123. O 123.1 123.2 123.3 123.4

123.5 123.6 123.7 123.8 123.9

124.0 124.1 124.2 124.3 124.4

124.5 124.6 124.7 124.8 124.9

125. O

Products )


Base API Gravity 95.0 95.1 95.2 95.3 95.4 95.5 95.6


0.94615 0.94606 O. 94597 O. 94588 0.94579

O. 94570 O. 94561 O. 94551 O. 94542 O. 94533

O. 94524 O. 94515 O. 94506 0.94497 O. 94488

0.94479 0.94470 0.94461 O. 94451 O. 94442

O. 94433 O. 94424 0.94415 0.94406 O. 94397

O. 94388 0.94379 O. 94370 O. 94361 O. 94351

O. 94342 O. 94333 O. 94324 O. 94315 O. 94306

O. 94297 O. 94288 0.94279 O. 94270 O. 94261

O. 94251 O. 94242 O. 94233 O. 94224 O. 94215

O. 94206 0.94197 O. 94188 0.94179 0.94170

0.94160

0.94611 O. 94602 O. 94593 O. 94584 O. 94575

O. 94566 O. 94557 O. 94548 O. 94539 0.94529

O. 94520 O. 94511 O. 94502 0.94493 O. 94484

0.94475 0.94466 O. 94457 0.94448 0.94439

0.94429 O. 94420 0.94411 O. 94402 O. 94393

O. 94384 O. 94375 O. 94366 O. 94357 O. 94348

O. 94338 0.94329 O. 94320 O. 94311 O. 94302

O. 94293 O. 94284 O. 94275 O. 94266 O. 94257

O. 94247 O. 94238 O. 94229 O. 94220 O. 94211

O. 94202 0.94193 O. 94184 0.94175 0.94165

0.94156

O. 94608 O. 94598 O. 94589 O. 94580 O. 94571

O. 94562 O. 94553 O. 94544 O. 94535 0.94526

O. 94517 O. 94507 0.94498 0.94489 O. 94480

0.94471 0.94462 O. 94453 0.94444 O. 94435

0.94426 0.94416 O. 94407 O. 94398 O. 94389

O. 94380 O. 94371 O. 94362 O. 94353 O. 94344

O. 94334 O. 94325 0.94316 O. 94307 O. 94298

O. 94289 O. 94280 O. 94271 0.94262 O. 94253

O. 94243 O. 94234 O. 94225 0.94216 O. 94207

0.94198 0.94189 O. 94180 0.94171 0.94161

O. 94152

O. 94604 O. 94595 O. 94586 0.94576 O. 94567

O. 94558 0.94549 O. 94540 O. 94531 O. 94522

O. 94513 O. 94504 0.94495 O. 94485 0.94476

0.94467 O. 94458 0.94449 0.94440 O. 94431

O. 94422 0.94413 O. 94403 O. 94394 O. 94385

0.94376 O. 94367 O. 94358 0.94349 O. 94340

O. 94331 O. 94321 O. 94312 O. 94303 O. 94294

O. 94285 0.94276 O. 94267 O. 94258 0.94249

O. 94239 O. 94230 O. 94221 O. 94212 O. 94203

0.94194 O. 94185 0.94176 0.94166 O. 94157

0.94148

O. 94600 O. 94591 O. 94582 O. 94573 O. 94564

O. 94554 O. 94545 O. 94536 O. 94527 O. 94518

O. 94509 O. 94500 0.94491 O. 94482 O. 94472

0.94463 O. 94454 0.94445 0.94436 O. 94427

0.94418 0.94409 O. 94400 O. 94390 O. 94381

O. 94372 O. 94363 O. 94354 O. 94345 O. 94336

O. 94327 O. 94317 O. 94308 0.94299 O. 94290

O. 94281 O. 94272 O. 94263 O. 94254 O. 94245

O. 94235 O. 94226 O. 94217 O. 94208 0.94199

0.94190 O. 94181 O. 94172 0.94162 O. 94153

0.94144

0.94596 O. 94587 O. 94578 O. 94569 O. 94560

O. 94551 O. 94542 O. 94532 O. 94523 O. 94514

O. 94505 0.94496 O. 94487 0.94478 0.94469

0.94460 O. 94450 0.94441 O. 94432 O. 94423

0.94414 O. 94405 0.94396 O. 94387 O. 94377

O. 94368 O. 94359 O. 94350 O. 94341 O. 94332

O. 94323 O. 94314 O. 94304 O. 94295 O. 94286

O. 94277 O. 94268 O. 94259 O. 94250 O. 94241

O. 94231 O. 94222 O. 94213 O. 94204 0.94195

0.94186 0.94177 0.94167 O. 94158 0.94149

0.94140

O. 94593 O. 94583 O. 94574 O. 94565 O. 94556

O. 94547 O. 94538 0.94529 O. 94520 O. 94510

O. 94501 0.94492 O. 94483 0.94474 0.94465

0.94456 0.94447 O. 94437 O. 94428 0.94419

0.94410 O. 94401 O. 94392 O. 94383 O. 94373

O. 94364 O. 94355 0.94346 O. 94337 O. 94328

0.94319 O. 94310 O. 94300 O. 94291 O. 94282

O. 94273 O. 94264 O. 94255 0.94246 O. 94237

O. 94227 O. 94218 O. 94209 O. 94200 0.94191

O. 94182 0.94173 0.94163 O. 94154 0.94145

0.94136

(Refined

OF

120. o 120.1 120.2 120.3 120.4

120.5 120.6 120.7 120.8 120.9

121.0 121.1 121.2 121.3 121.4

121.5 121.6 121.7 121.8 121.9

122. o 122.1 122.2 122.3 122.4

122.5 122.6 122.7 122.8 122.9

123. O 123.1 123.2 123.3 123.4

123.5 123.6 123.7 123.8 123.9

124.0 124.1 124.2 124.3 124.4

124.5 124.6 124.7 124.8 124.9

125. O



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.5 Instructions to Generate Tables 6D - Correction of Volume to 60°F Against API Gravity at 60°F for Generalized Lubricating Oils

Input Variables: Base M I gravity and temperature. Pressure set to O psig.


Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:


Increment base API gravity value by 0.1'MI in range of -10.0" to 45.O'MI. Ensure that the base M I gravity value remains rounded consistent with instructions in 1 1.1.5.4.



Determine the CTL value using procedure in 1 1.1.6.1 & specifjdng commodity group "D." Round the CTL value consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 6D. Volume Correction Factor Due to Temperature Against API Gravity at 60'F (Lube Oils)


Base API Gravity OF 3 5 . 0 3 5 . 1 3 5 . 2 3 5 . 3 35 .4 3 5 . 5 3 5 . 6 OF


1 2 0 . o 1 2 0 . 1 1 2 0 . 2 1 2 0 . 3 1 2 0 . 4

1 2 0 . 5 1 2 0 . 6 1 2 0 . 7 1 2 0 . 8 1 2 0 . 9

1 2 1 . 0 1 2 1 . 1 1 2 1 . 2 1 2 1 . 3 1 2 1 . 4

1 2 1 . 5 1 2 1 . 6 1 2 1 . 7 1 2 1 . 8 1 2 1 . 9

1 2 2 . o 1 2 2 . 1 1 2 2 . 2 1 2 2 . 3 1 2 2 . 4

1 2 2 . 5 1 2 2 . 6 1 2 2 . 7 1 2 2 . 8 1 2 2 . 9

1 2 3 . O 1 2 3 . 1 1 2 3 . 2 1 2 3 . 3 1 2 3 . 4

1 2 3 . 5 1 2 3 . 6 1 2 3 . 7 1 2 3 . 8 1 2 3 . 9

1 2 4 . 0 1 2 4 . 1 1 2 4 . 2 1 2 4 . 3 1 2 4 . 4

1 2 4 . 5 1 2 4 . 6 1 2 4 . 7 1 2 4 . 8 1 2 4 . 9

1 2 5 . O

O . 9 7 5 1 7 O . 9 7 5 1 3 O . 9 7 5 0 9 O . 9 7 5 0 5 O . 9 7 5 0 1

0 . 9 7 4 9 6 0 . 9 7 4 9 2 O . 9 7 4 8 8 O . 9 7 4 8 4 O . 9 7 4 8 0

0 . 9 7 4 7 6 0 . 9 7 4 7 1 0 . 9 7 4 6 7 0 . 9 7 4 6 3 0 . 9 7 4 5 9

O . 9 7 4 5 5 O . 9 7 4 5 1 0 . 9 7 4 4 6 O . 9 7 4 4 2 O . 9 7 4 3 8

O . 9 7 4 3 4 O . 9 7 4 3 0 0 . 9 7 4 2 6 O . 9 7 4 2 1 0 . 9 7 4 1 7

0 . 9 7 4 1 3 0 . 9 7 4 0 9 O . 9 7 4 0 5 O . 9 7 4 0 1 0 . 9 7 3 9 6

O . 9 7 3 9 2 O . 9 7 3 8 8 O . 9 7 3 8 4 O . 9 7 3 8 0 0 . 9 7 3 7 6

O . 9 7 3 7 1 O . 9 7 3 6 7 O . 9 7 3 6 3 O . 9 7 3 5 9 O . 9 7 3 5 5

O . 9 7 3 5 1 0 . 9 7 3 4 6 O . 9 7 3 4 2 O . 9 7 3 3 8 O . 9 7 3 3 4

O . 9 7 3 3 0 0 . 9 7 3 2 6 O . 9 7 3 2 1 O . 9 7 3 1 7 O . 9 7 3 1 3

O . 9 7 3 0 9

0 . 9 7 5 1 6 O . 9 7 5 1 2 O . 9 7 5 0 7 O . 9 7 5 0 3 0 . 9 7 4 9 9

0 . 9 7 4 9 5 0 . 9 7 4 9 1 O . 9 7 4 8 7 O . 9 7 4 8 2 0 . 9 7 4 7 8

0 . 9 7 4 7 4 0 . 9 7 4 7 0 0 . 9 7 4 6 6 0 . 9 7 4 6 2 O . 9 7 4 5 7

O . 9 7 4 5 3 0 . 9 7 4 4 9 0 . 9 7 4 4 5 0 . 9 7 4 4 1 O . 9 7 4 3 7

O . 9 7 4 3 2 O . 9 7 4 2 8 O . 9 7 4 2 4 O . 9 7 4 2 0 0 . 9 7 4 1 6

0 . 9 7 4 1 1 O . 9 7 4 0 7 O . 9 7 4 0 3 0 . 9 7 3 9 9 O . 9 7 3 9 5

O . 9 7 3 9 1 O . 9 7 3 8 6 O . 9 7 3 8 2 O . 9 7 3 7 8 O . 9 7 3 7 4

O . 9 7 3 7 0 O . 9 7 3 6 6 O . 9 7 3 6 1 O . 9 7 3 5 7 O . 9 7 3 5 3

0 . 9 7 3 4 9 O . 9 7 3 4 5 O . 9 7 3 4 1 O . 9 7 3 3 6 O . 9 7 3 3 2

O . 9 7 3 2 8 O . 9 7 3 2 4 O . 9 7 3 2 0 0 . 9 7 3 1 6 O . 9 7 3 1 1

O . 9 7 3 0 7

O . 9 7 5 1 4 O . 9 7 5 1 0 O . 9 7 5 0 6 O . 9 7 5 0 2 0 . 9 7 4 9 8

0 . 9 7 4 9 3 0 . 9 7 4 8 9 O . 9 7 4 8 5 O . 9 7 4 8 1 0 . 9 7 4 7 7

0 . 9 7 4 7 3 0 . 9 7 4 6 8 0 . 9 7 4 6 4 0 . 9 7 4 6 0 0 . 9 7 4 5 6

O . 9 7 4 5 2 0 . 9 7 4 4 7 0 . 9 7 4 4 3 0 . 9 7 4 3 9 O . 9 7 4 3 5

O . 9 7 4 3 1 O . 9 7 4 2 7 O . 9 7 4 2 2 0 . 9 7 4 1 8 0 . 9 7 4 1 4

0 . 9 7 4 1 0 0 . 9 7 4 0 6 O . 9 7 4 0 2 O . 9 7 3 9 7 O . 9 7 3 9 3

O . 9 7 3 8 9 O . 9 7 3 8 5 O . 9 7 3 8 1 O . 9 7 3 7 7 O . 9 7 3 7 2

O . 9 7 3 6 8 O . 9 7 3 6 4 O . 9 7 3 6 0 O . 9 7 3 5 6 O . 9 7 3 5 2

O . 9 7 3 4 7 O . 9 7 3 4 3 O . 9 7 3 3 9 O . 9 7 3 3 5 O . 9 7 3 3 1

0 . 9 7 3 2 6 O . 9 7 3 2 2 O . 9 7 3 1 8 O . 9 7 3 1 4 O . 9 7 3 1 0

O . 9 7 3 0 6

O . 9 7 5 1 3 O . 9 7 5 0 9 O . 9 7 5 0 4 O . 9 7 5 0 0 0 . 9 7 4 9 6

0 . 9 7 4 9 2 O . 9 7 4 8 8 O . 9 7 4 8 4 0 . 9 7 4 7 9 0 . 9 7 4 7 5

0 . 9 7 4 7 1 0 . 9 7 4 6 7 0 . 9 7 4 6 3 O . 9 7 4 5 8 O . 9 7 4 5 4

O . 9 7 4 5 0 0 . 9 7 4 4 6 O . 9 7 4 4 2 O . 9 7 4 3 8 O . 9 7 4 3 3

0 . 9 7 4 2 9 O . 9 7 4 2 5 O . 9 7 4 2 1 0 . 9 7 4 1 7 0 . 9 7 4 1 3

O . 9 7 4 0 8 O . 9 7 4 0 4 O . 9 7 4 0 0 0 . 9 7 3 9 6 O . 9 7 3 9 2

O . 9 7 3 8 7 O . 9 7 3 8 3 0 . 9 7 3 7 9 O . 9 7 3 7 5 O . 9 7 3 7 1

O . 9 7 3 6 7 O . 9 7 3 6 2 O . 9 7 3 5 8 O . 9 7 3 5 4 O . 9 7 3 5 0

0 . 9 7 3 4 6 O . 9 7 3 4 2 O . 9 7 3 3 7 O . 9 7 3 3 3 0 . 9 7 3 2 9

O . 9 7 3 2 5 O . 9 7 3 2 1 O . 9 7 3 1 7 O . 9 7 3 1 2 O . 9 7 3 0 8

O . 9 7 3 0 4

O . 9 7 5 1 1 O . 9 7 5 0 7 O . 9 7 5 0 3 0 . 9 7 4 9 9 0 . 9 7 4 9 5

0 . 9 7 4 9 0 0 . 9 7 4 8 6 O . 9 7 4 8 2 0 . 9 7 4 7 8 0 . 9 7 4 7 4

0 . 9 7 4 6 9 0 . 9 7 4 6 5 0 . 9 7 4 6 1 O . 9 7 4 5 7 O . 9 7 4 5 3

0 . 9 7 4 4 9 0 . 9 7 4 4 4 0 . 9 7 4 4 0 0 . 9 7 4 3 6 O . 9 7 4 3 2

O . 9 7 4 2 8 O . 9 7 4 2 4 0 . 9 7 4 1 9 0 . 9 7 4 1 5 0 . 9 7 4 1 1

O . 9 7 4 0 7 O . 9 7 4 0 3 O . 9 7 3 9 8 O . 9 7 3 9 4 O . 9 7 3 9 0

O . 9 7 3 8 6 O . 9 7 3 8 2 O . 9 7 3 7 8 O . 9 7 3 7 3 O . 9 7 3 6 9

O . 9 7 3 6 5 O . 9 7 3 6 1 O . 9 7 3 5 7 O . 9 7 3 5 2 O . 9 7 3 4 8

O . 9 7 3 4 4 O . 9 7 3 4 0 O . 9 7 3 3 6 O . 9 7 3 3 2 O . 9 7 3 2 7

O . 9 7 3 2 3 0 . 9 7 3 1 9 O . 9 7 3 1 5 O . 9 7 3 1 1 O . 9 7 3 0 7

O . 9 7 3 0 2

O . 9 7 5 1 0 O . 9 7 5 0 6 O . 9 7 5 0 1 0 . 9 7 4 9 7 0 . 9 7 4 9 3

0 . 9 7 4 8 9 O . 9 7 4 8 5 O . 9 7 4 8 0 0 . 9 7 4 7 6 O . 9 7 4 7 2

0 . 9 7 4 6 8 0 . 9 7 4 6 4 0 . 9 7 4 6 0 O . 9 7 4 5 5 O . 9 7 4 5 1

0 . 9 7 4 4 7 0 . 9 7 4 4 3 0 . 9 7 4 3 9 O . 9 7 4 3 4 O . 9 7 4 3 0

0 . 9 7 4 2 6 O . 9 7 4 2 2 0 . 9 7 4 1 8 0 . 9 7 4 1 4 0 . 9 7 4 0 9

O . 9 7 4 0 5 O . 9 7 4 0 1 O . 9 7 3 9 7 O . 9 7 3 9 3 O . 9 7 3 8 9

O . 9 7 3 8 4 O . 9 7 3 8 0 0 . 9 7 3 7 6 O . 9 7 3 7 2 O . 9 7 3 6 8

O . 9 7 3 6 3 O . 9 7 3 5 9 O . 9 7 3 5 5 O . 9 7 3 5 1 O . 9 7 3 4 7

O . 9 7 3 4 3 O . 9 7 3 3 8 O . 9 7 3 3 4 O . 9 7 3 3 0 0 . 9 7 3 2 6

O . 9 7 3 2 2 O . 9 7 3 1 7 O . 9 7 3 1 3 O . 9 7 3 0 9 O . 9 7 3 0 5

O . 9 7 3 0 1

O . 9 7 5 0 8 O . 9 7 5 0 4 O . 9 7 5 0 0 0 . 9 7 4 9 6 0 . 9 7 4 9 1

O . 9 7 4 8 7 O . 9 7 4 8 3 0 . 9 7 4 7 9 0 . 9 7 4 7 5 0 . 9 7 4 7 1

0 . 9 7 4 6 6 0 . 9 7 4 6 2 O . 9 7 4 5 8 O . 9 7 4 5 4 O . 9 7 4 5 0

0 . 9 7 4 4 5 0 . 9 7 4 4 1 O . 9 7 4 3 7 O . 9 7 4 3 3 0 . 9 7 4 2 9

O . 9 7 4 2 5 O . 9 7 4 2 0 0 . 9 7 4 1 6 O . 9 7 4 1 2 O . 9 7 4 0 8

O . 9 7 4 0 4 0 . 9 7 3 9 9 O . 9 7 3 9 5 O . 9 7 3 9 1 O . 9 7 3 8 7

O . 9 7 3 8 3 0 . 9 7 3 7 9 O . 9 7 3 7 4 O . 9 7 3 7 0 O . 9 7 3 6 6

O . 9 7 3 6 2 O . 9 7 3 5 8 O . 9 7 3 5 3 0 . 9 7 3 4 9 O . 9 7 3 4 5

O . 9 7 3 4 1 O . 9 7 3 3 7 O . 9 7 3 3 3 O . 9 7 3 2 8 O . 9 7 3 2 4

O . 9 7 3 2 0 0 . 9 7 3 1 6 O . 9 7 3 1 2 O . 9 7 3 0 7 O . 9 7 3 0 3

0 . 9 7 2 9 9

1 2 0 . o 1 2 0 . 1 1 2 0 . 2 1 2 0 . 3 1 2 0 . 4

1 2 0 . 5 1 2 0 . 6 1 2 0 . 7 1 2 0 . 8 1 2 0 . 9

1 2 1 . 0 1 2 1 . 1 1 2 1 . 2 1 2 1 . 3 1 2 1 . 4

1 2 1 . 5 1 2 1 . 6 1 2 1 . 7 1 2 1 . 8 1 2 1 . 9

1 2 2 . o 1 2 2 . 1 1 2 2 . 2 1 2 2 . 3 1 2 2 . 4

1 2 2 . 5 1 2 2 . 6 1 2 2 . 7 1 2 2 . 8 1 2 2 . 9

1 2 3 . O 1 2 3 . 1 1 2 3 . 2 1 2 3 . 3 1 2 3 . 4

1 2 3 . 5 1 2 3 . 6 1 2 3 . 7 1 2 3 . 8 1 2 3 . 9

1 2 4 . 0 1 2 4 . 1 1 2 4 . 2 1 2 4 . 3 1 2 4 . 4

1 2 4 . 5 1 2 4 . 6 1 2 4 . 7 1 2 4 . 8 1 2 4 . 9

1 2 5 . O



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.6 Instructions to Generate Table 23A - Correction of Observed Specific Gravity to Specific Gravity 6O/6O0F for Generalized Crude Oils

Input Variables: Observed relative density and temperature. Pressure set to O psig.

Output Variables: Relative density (60/60’F).

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step7:


Increment observed relative density value by 0.0001 in range of 0.4710 to 1.1989. Ensure that the observed relative density value remains rounded consistent with instructions in 1 1.1.5.4.

Increment observed temperature by 0.1’F in range of -58.0” to 302.0’F. Ensure that the observed temperature value remains rounded consistent with instructions in 1 1.1.5.4.

Convert density units from relative density to kg/m3 using procedure in 1 1.1.5.1.

Determine the base density using procedure in 1 1.1.6.2 & specifjdng commodity group “A.”

Convert the density units from kg/m3 back to relative density (60/60’F) using procedure in 1 1.1.5.1. Round the value of this relative density consistent with instructions in 11.1.5.4.

Increment the value of the relative density or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of relative density and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


Table 23A. Correction of Observed Relative Density to Base Relative Density (6O/6O0F) (Crude Oils)

If hydrometer used to determine density, apply glass correction before entering table

OF

90.0 90.1 90.2 90.3 90.4

90.5 90.6 90.7 90.8 90.9

91.0 91.1 91.2 91.3 91.4

91.5 91.6 91.7 91.8 91.9

92.0 92.1 92.2 92.3 92.4

92.5 92.6 92.7 92.8 92.9

93.0 93.1 93.2 93.3 93.4

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

94.5 94.6 94.7 94.8 94.9

95.0


Observed Relative Density (60/60) 0.8270 0.8271 0.8272 0.8273 0.8274 0.8275 0.8276

Corresponding Density at 60'F & O psig, Relative Density (60/60)

O. 8393 O. 8393 O. 8394 O. 8394 O. 8394

O. 8395 O. 8395 O. 8396 O. 8396 O. 8396

O. 8397 O. 8397 O. 8398 O. 8398 O. 8398

O. 8399 O. 8399 O. 8400 O. 8400 O. 8400

O. 8401 O. 8401 O. 8402 O. 8402 O. 8402

O. 8403 O. 8403 O. 8404 O. 8404 O. 8404

O. 8405 O. 8405 O. 8406 O. 8406 O. 8406

O. 8407 O. 8407 O. 8408 O. 8408 O. 8408

O. 8409 O. 8409 O. 8410 O. 8410 O. 8410

O. 8411 O. 8411 O. 8412 O. 8412 O. 8413

O. 8413

O. 8394 O. 8394 O. 8395 O. 8395 O. 8395

O. 8396 O. 8396 O. 8397 O. 8397 O. 8397

O. 8398 O. 8398 O. 8399 O. 8399 O. 8399

O. 8400 O. 8400 O. 8401 O. 8401 O. 8401

O. 8402 O. 8402 O. 8403 O. 8403 O. 8403

O. 8404 O. 8404 O. 8405 O. 8405 O. 8405

O. 8406 O. 8406 O. 8407 O. 8407 O. 8407

O. 8408 O. 8408 O. 8409 O. 8409 O. 8409

O. 8410 O. 8410 O. 8411 O. 8411 O. 8411

O. 8412 O. 8412 O. 8413 O. 8413 O. 8413

O. 8414

O. 8395 O. 8395 O. 8395 O. 8396 O. 8396

O. 8397 O. 8397 O. 8398 O. 8398 O. 8398

O. 8399 O. 8399 O. 8400 O. 8400 O. 8400

O. 8401 O. 8401 O. 8402 O. 8402 O. 8402

O. 8403 O. 8403 O. 8404 O. 8404 O. 8404

O. 8405 O. 8405 O. 8406 O. 8406 O. 8406

O. 8407 O. 8407 O. 8408 O. 8408 O. 8408

O. 8409 O. 8409 O. 8410 O. 8410 O. 8410

O. 8411 O. 8411 O. 8412 O. 8412 O. 8412

O. 8413 O. 8413 O. 8414 O. 8414 O. 8414

O. 8415

O. 8396 O. 8396 O. 8396 O. 8397 O. 8397

O. 8398 O. 8398 O. 8399 O. 8399 O. 8399

O. 8400 O. 8400 O. 8401 O. 8401 O. 8401

O. 8402 O. 8402 O. 8403 O. 8403 O. 8403

O. 8404 O. 8404 O. 8405 O. 8405 O. 8405

O. 8406 O. 8406 O. 8407 O. 8407 O. 8407

O. 8408 O. 8408 O. 8409 O. 8409 O. 8409

O. 8410 O. 8410 O. 8411 O. 8411 O. 8411

O. 8412 O. 8412 O. 8413 O. 8413 O. 8413

O. 8414 O. 8414 O. 8415 O. 8415 O. 8415

0.8416

O. 8397 O. 8397 O. 8397 O. 8398 O. 8398

O. 8399 O. 8399 O. 8399 O. 8400 O. 8400

O. 8401 O. 8401 O. 8402 O. 8402 O. 8402

O. 8403 O. 8403 O. 8404 O. 8404 O. 8404

O. 8405 O. 8405 O. 8406 O. 8406 O. 8406

O. 8407 O. 8407 O. 8408 O. 8408 O. 8408

O. 8409 O. 8409 O. 8410 O. 8410 O. 8410

O. 8411 O. 8411 O. 8412 O. 8412 O. 8412

O. 8413 O. 8413 O. 8414 O. 8414 O. 8414

O. 8415 O. 8415 0.8416 0.8416 0.8416

O. 8417

O. 8398 O. 8398 O. 8398 O. 8399 O. 8399

O. 8400 O. 8400 O. 8400 O. 8401 O. 8401

O. 8402 O. 8402 O. 8402 O. 8403 O. 8403

O. 8404 O. 8404 O. 8405 O. 8405 O. 8405

O. 8406 O. 8406 O. 8407 O. 8407 O. 8407

O. 8408 O. 8408 O. 8409 O. 8409 O. 8409

O. 8410 O. 8410 O. 8411 O. 8411 O. 8411

O. 8412 O. 8412 O. 8413 O. 8413 O. 8413

O. 8414 O. 8414 O. 8415 O. 8415 O. 8415

0.8416 0.8416 O. 8417 O. 8417 O. 8417

O. 8418

O. 8399 O. 8399 O. 8399 O. 8400 O. 8400

O. 8401 O. 8401 O. 8401 O. 8402 O. 8402

O. 8403 O. 8403 O. 8403 O. 8404 O. 8404

O. 8405 O. 8405 O. 8405 O. 8406 O. 8406

O. 8407 O. 8407 O. 8408 O. 8408 O. 8408

O. 8409 O. 8409 O. 8410 O. 8410 O. 8410

O. 8411 O. 8411 O. 8412 O. 8412 O. 8412

O. 8413 O. 8413 O. 8414 O. 8414 O. 8414

O. 8415 O. 8415 0.8416 0.8416 0.8416

O. 8417 O. 8417 O. 8418 O. 8418 O. 8418

0.8419

90.0 90.1 90.2 90.3 90.4

90.5 90.6 90.7 90.8 90.9

91.0 91.1 91.2 91.3 91.4

91.5 91.6 91.7 91.8 91.9

92.0 92.1 92.2 92.3 92.4

92.5 92.6 92.7 92.8 92.9

93.0 93.1 93.2 93.3 93.4

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

94.5 94.6 94.7 94.8 94.9

95.0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.7 Instructions to Generate Table 23B - Correction of Observed Specific Gravity to Specific Gravity 6O/6O0F for Generalized Products


Output Variables: Relative density (60/60'F).

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step7:


Increment observed relative density value by 0.0001 in range of 0.4709 to 1.2065. Ensure that the observed relative density value remains rounded consistent with instructions in 1 1.1.5.4.



Determine the base density using procedure in 11.1.6.2 & specifjdng commodity group "B."

Convert the density units from kg/m3 back to relative density (60/60'F) using procedure in 1 1.1.5.1. Round the value of this relative density consistent with instructions in 11.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 23B. Correction of Observed Relative Density to Base Relative Density (6O/6O0F) (Refined Products )

If hydrometer used to determine density, apply glass correction before entering table

OF

90.0 90.1 90.2 90.3 90.4

90.5 90.6 90.7 90.8 90.9

91.0 91.1 91.2 91.3 91.4

91.5 91.6 91.7 91.8 91.9

92.0 92.1 92.2 92.3 92.4

92.5 92.6 92.7 92.8 92.9

93.0 93.1 93.2 93.3 93.4

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

94.5 94.6 94.7 94.8 94.9

95.0


Observed Relative Density (60/60) 0.8270 0.8271 0.8272 0.8273 0.8274 0.8275 0.8276

Corresponding Density at 60'F & O psig, Relative Density (60/60)

O. 8389 O. 8389 O. 8390 O. 8390 O. 8390

O. 8391 O. 8391 O. 8392 O. 8392 O. 8392

O. 8393 O. 8393 O. 8394 O. 8394 O. 8394

O. 8395 O. 8395 O. 8396 O. 8396 O. 8396

O. 8397 O. 8397 O. 8398 O. 8398 O. 8398

O. 8399 O. 8399 O. 8400 O. 8400 O. 8400

O. 8401 O. 8401 O. 8402 O. 8402 O. 8402

O. 8403 O. 8403 O. 8403 O. 8404 O. 8404

O. 8405 O. 8405 O. 8405 O. 8406 O. 8406

O. 8407 O. 8407 O. 8407 O. 8408 O. 8408

O. 8409

O. 8390 O. 8390 O. 8391 O. 8391 O. 8391

O. 8392 O. 8392 O. 8393 O. 8393 O. 8393

O. 8394 O. 8394 O. 8395 O. 8395 O. 8395

O. 8396 O. 8396 O. 8397 O. 8397 O. 8397

O. 8398 O. 8398 O. 8399 O. 8399 O. 8399

O. 8400 O. 8400 O. 8401 O. 8401 O. 8401

O. 8402 O. 8402 O. 8403 O. 8403 O. 8403

O. 8404 O. 8404 O. 8404 O. 8405 O. 8405

O. 8406 O. 8406 O. 8406 O. 8407 O. 8407

O. 8408 O. 8408 O. 8408 O. 8409 O. 8409

O. 8410

O. 8391 O. 8391 O. 8392 O. 8392 O. 8392

O. 8393 O. 8393 O. 8394 O. 8394 O. 8394

O. 8395 O. 8395 O. 8396 O. 8396 O. 8396

O. 8397 O. 8397 O. 8398 O. 8398 O. 8398

O. 8399 O. 8399 O. 8400 O. 8400 O. 8400

O. 8401 O. 8401 O. 8402 O. 8402 O. 8402

O. 8403 O. 8403 O. 8404 O. 8404 O. 8404

O. 8405 O. 8405 O. 8405 O. 8406 O. 8406

O. 8407 O. 8407 O. 8407 O. 8408 O. 8408

O. 8409 O. 8409 O. 8409 O. 8410 O. 8410

O. 8411

O. 8392 O. 8392 O. 8393 O. 8393 O. 8393

O. 8394 O. 8394 O. 8395 O. 8395 O. 8395

O. 8396 O. 8396 O. 8397 O. 8397 O. 8397

O. 8398 O. 8398 O. 8399 O. 8399 O. 8399

O. 8400 O. 8400 O. 8401 O. 8401 O. 8401

O. 8402 O. 8402 O. 8403 O. 8403 O. 8403

O. 8404 O. 8404 O. 8405 O. 8405 O. 8405

O. 8406 O. 8406 O. 8406 O. 8407 O. 8407

O. 8408 O. 8408 O. 8408 O. 8409 O. 8409

O. 8410 O. 8410 O. 8410 O. 8411 O. 8411

O. 8412

O. 8393 O. 8393 O. 8394 O. 8394 O. 8394

O. 8395 O. 8395 O. 8396 O. 8396 O. 8396

O. 8397 O. 8397 O. 8398 O. 8398 O. 8398

O. 8399 O. 8399 O. 8400 O. 8400 O. 8400

O. 8401 O. 8401 O. 8402 O. 8402 O. 8402

O. 8403 O. 8403 O. 8404 O. 8404 O. 8404

O. 8405 O. 8405 O. 8405 O. 8406 O. 8406

O. 8407 O. 8407 O. 8407 O. 8408 O. 8408

O. 8409 O. 8409 O. 8409 O. 8410 O. 8410

O. 8411 O. 8411 O. 8411 O. 8412 O. 8412

O. 8413

O. 8394 O. 8394 O. 8395 O. 8395 O. 8395

O. 8396 O. 8396 O. 8397 O. 8397 O. 8397

O. 8398 O. 8398 O. 8399 O. 8399 O. 8399

O. 8400 O. 8400 O. 8401 O. 8401 O. 8401

O. 8402 O. 8402 O. 8403 O. 8403 O. 8403

O. 8404 O. 8404 O. 8405 O. 8405 O. 8405

O. 8406 O. 8406 O. 8406 O. 8407 O. 8407

O. 8408 O. 8408 O. 8408 O. 8409 O. 8409

O. 8410 O. 8410 O. 8410 O. 8411 O. 8411

O. 8412 O. 8412 O. 8412 O. 8413 O. 8413

O. 8414

O. 8395 O. 8395 O. 8396 O. 8396 O. 8396

O. 8397 O. 8397 O. 8398 O. 8398 O. 8398

O. 8399 O. 8399 O. 8400 O. 8400 O. 8400

O. 8401 O. 8401 O. 8402 O. 8402 O. 8402

O. 8403 O. 8403 O. 8404 O. 8404 O. 8404

O. 8405 O. 8405 O. 8406 O. 8406 O. 8406

O. 8407 O. 8407 O. 8407 O. 8408 O. 8408

O. 8409 O. 8409 O. 8409 O. 8410 O. 8410

O. 8411 O. 8411 O. 8411 O. 8412 O. 8412

O. 8413 O. 8413 O. 8413 O. 8414 O. 8414

O. 8415

90.0 90.1 90.2 90.3 90.4

90.5 90.6 90.7 90.8 90.9

91.0 91.1 91.2 91.3 91.4

91.5 91.6 91.7 91.8 91.9

92.0 92.1 92.2 92.3 92.4

92.5 92.6 92.7 92.8 92.9

93.0 93.1 93.2 93.3 93.4

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

94.5 94.6 94.7 94.8 94.9

95.0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.8 Instructions to Generate Table 23D - Correction of Observed Specific Gravity to Specific Gravity 6O/6O0F for Generalized Lubricating Oils


Output Variables: Relative density (60/60’F).

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step7:


Increment observed relative density value by 0.0001 in range of 0.715 1 to 1.2053. Ensure that the observed relative density value remains rounded consistent with instructions in 1 1.1.5.4.

Increment observed temperature by 0.1’F in range of -58.0” to 302.0’F. Ensure that the observed temperature value remains rounded consistent with instructions in 1 1.1.5.4.


Determine the base density using procedure in 11.1.6.2 & specifjdng commodity group “AD.”

Convert the density units from kg/m3 back to relative density (60/60’F) using procedure in 1 1.1.5.1. Round the value of this relative density consistent with instructions in 11.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 23D. Correction of Observed Relative Density to Base Relative Density (6O/6O0F) (Lube Oils) If hydrometer used to determine density, apply glass correction before entering table

OF

90.0 90.1 90.2 90.3 90.4

90.5 90.6 90.7 90.8 90.9

91.0 91.1 91.2 91.3 91.4

91.5 91.6 91.7 91.8 91.9

92.0 92.1 92.2 92.3 92.4

92.5 92.6 92.7 92.8 92.9

93.0 93.1 93.2 93.3 93.4

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

94.5 94.6 94.7 94.8 94.9

95.0


Observed Relative Density (60/60) 0.8270 0.8271 0.8272 0.8273 0.8274 0.8275

Corresponding Density at 60'F & O psig, Relative Density

O. 8375 O. 8375 0.8376 0.8376 O. 8377

O. 8377 O. 8377 O. 8378 O. 8378 O. 8378

0.8379 0.8379 0.8379 O. 8380 O. 8380

O. 8380 O. 8381 O. 8381 O. 8381 O. 8382

O. 8382 O. 8383 O. 8383 O. 8383 O. 8384

O. 8384 O. 8384 O. 8385 O. 8385 O. 8385

O. 8386 O. 8386 O. 8386 O. 8387 O. 8387

O. 8387 O. 8388 O. 8388 O. 8389 O. 8389

O. 8389 O. 8390 O. 8390 O. 8390 O. 8391

O. 8391 O. 8391 O. 8392 O. 8392 O. 8392

O. 8393

0.8376 0.8376 O. 8377 O. 8377 O. 8378

O. 8378 O. 8378 0.8379 0.8379 0.8379

O. 8380 O. 8380 O. 8380 O. 8381 O. 8381

O. 8381 O. 8382 O. 8382 O. 8382 O. 8383

O. 8383 O. 8384 O. 8384 O. 8384 O. 8385

O. 8385 O. 8385 O. 8386 O. 8386 O. 8386

O. 8387 O. 8387 O. 8387 O. 8388 O. 8388

O. 8388 O. 8389 O. 8389 O. 8390 O. 8390

O. 8390 O. 8391 O. 8391 O. 8391 O. 8392

O. 8392 O. 8392 O. 8393 O. 8393 O. 8393

O. 8394

O. 8377 O. 8377 O. 8378 O. 8378 0.8379

0.8379 0.8379 O. 8380 O. 8380 O. 8380

O. 8381 O. 8381 O. 8381 O. 8382 O. 8382

O. 8382 O. 8383 O. 8383 O. 8383 O. 8384

O. 8384 O. 8385 O. 8385 O. 8385 O. 8386

O. 8386 O. 8386 O. 8387 O. 8387 O. 8387

O. 8388 O. 8388 O. 8388 O. 8389 O. 8389

O. 8389 O. 8390 O. 8390 O. 8391 O. 8391

O. 8391 O. 8392 O. 8392 O. 8392 O. 8393

O. 8393 O. 8393 O. 8394 O. 8394 O. 8394

O. 8395

O. 8378 O. 8378 0.8379 0.8379 O. 8380

O. 8380 O. 8380 O. 8381 O. 8381 O. 8381

O. 8382 O. 8382 O. 8382 O. 8383 O. 8383

O. 8383 O. 8384 O. 8384 O. 8384 O. 8385

O. 8385 O. 8386 O. 8386 O. 8386 O. 8387

O. 8387 O. 8387 O. 8388 O. 8388 O. 8388

O. 8389 O. 8389 O. 8389 O. 8390 O. 8390

O. 8390 O. 8391 O. 8391 O. 8392 O. 8392

O. 8392 O. 8393 O. 8393 O. 8393 O. 8394

O. 8394 O. 8394 O. 8395 O. 8395 O. 8395

O. 8396

0.8379 0.8379 O. 8380 O. 8380 O. 8381

O. 8381 O. 8381 O. 8382 O. 8382 O. 8382

O. 8383 O. 8383 O. 8383 O. 8384 O. 8384

O. 8384 O. 8385 O. 8385 O. 8385 O. 8386

O. 8386 O. 8387 O. 8387 O. 8387 O. 8388

O. 8388 O. 8388 O. 8389 O. 8389 O. 8389

O. 8390 O. 8390 O. 8390 O. 8391 O. 8391

O. 8391 O. 8392 O. 8392 O. 8393 O. 8393

O. 8393 O. 8394 O. 8394 O. 8394 O. 8395

O. 8395 O. 8395 O. 8396 O. 8396 O. 8396

O. 8397

O. 8380 O. 8380 O. 8381 O. 8381 O. 8382

O. 8382 O. 8382 O. 8383 O. 8383 O. 8383

O. 8384 O. 8384 O. 8384 O. 8385 O. 8385

O. 8385 O. 8386 O. 8386 O. 8386 O. 8387

O. 8387 O. 8388 O. 8388 O. 8388 O. 8389

O. 8389 O. 8389 O. 8390 O. 8390 O. 8390

O. 8391 O. 8391 O. 8391 O. 8392 O. 8392

O. 8392 O. 8393 O. 8393 O. 8394 O. 8394

O. 8394 O. 8395 O. 8395 O. 8395 O. 8396

O. 8396 O. 8396 O. 8397 O. 8397 O. 8397

O. 8398

0.8276

(60/60)

O. 8381 O. 8381 O. 8382 O. 8382 O. 8383

O. 8383 O. 8383 O. 8384 O. 8384 O. 8384

O. 8385 O. 8385 O. 8385 O. 8386 O. 8386

O. 8386 O. 8387 O. 8387 O. 8387 O. 8388

O. 8388 O. 8389 O. 8389 O. 8389 O. 8390

O. 8390 O. 8390 O. 8391 O. 8391 O. 8391

O. 8392 O. 8392 O. 8392 O. 8393 O. 8393

O. 8393 O. 8394 O. 8394 O. 8395 O. 8395

O. 8395 O. 8396 O. 8396 O. 8396 O. 8397

O. 8397 O. 8397 O. 8398 O. 8398 O. 8398

O. 8399

OF

90.0 90.1 90.2 90.3 90.4

90.5 90.6 90.7 90.8 90.9

91.0 91.1 91.2 91.3 91.4

91.5 91.6 91.7 91.8 91.9

92.0 92.1 92.2 92.3 92.4

92.5 92.6 92.7 92.8 92.9

93.0 93.1 93.2 93.3 93.4

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

94.5 94.6 94.7 94.8 94.9

95.0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.9 Instructions to Generate Tables 24A and 24B - Correction of Volume to 60°F Against Specific Gravity 60/60”F for Generalized Crude Oils and Products

Input Variables: Base relative density (60/60’F) and temperature. Pressure set to O psig.


Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:


Increment relative density (60/60’F) value by 0.000 1 in range of 0.6 1 13 to 1.1646. Ensure that the base relative density value remains rounded consistent with instructions in 1 1.1.5.4.

Increment temperature by 0.1’F in range of -58.0” to 302’F. Ensure that the temperature value remains rounded consistent with instructions in 1 1.1.5.4.


Determine the CTL value using procedure in 11.1.6.1 & specifjdng commodity group “A” or “B” as appropriate. Round the CTL value consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 24A. Volume Correction Factor Due to Temperature Against Relative Density at 60'F (Crude Oils)


Base Relative Density ( 6 0 / 6 0 ) OF 0 . 9 2 5 0 0 . 9 2 5 1 0 . 9 2 5 2 0 . 9 2 5 3 0 . 9 2 5 4 0 . 9 2 5 5 0 . 9 2 5 6 OF


1 0 5 . O 1 0 5 . 1 1 0 5 . 2 1 0 5 . 3 1 0 5 . 4

1 0 5 . 5 1 0 5 . 6 1 0 5 . 7 1 0 5 . 8 1 0 5 . 9

1 0 6 . 0 1 0 6 . 1 1 0 6 . 2 1 0 6 . 3 1 0 6 . 4

1 0 6 . 5 1 0 6 . 6 1 0 6 . 7 1 0 6 . 8 1 0 6 . 9

1 0 7 . 0 1 0 7 . 1 1 0 7 . 2 1 0 7 . 3 1 0 7 . 4

1 0 7 . 5 1 0 7 . 6 1 0 7 . 7 1 0 7 . 8 1 0 7 . 9

1 0 8 . O 1 0 8 . 1 1 0 8 . 2 1 0 8 . 3 1 0 8 . 4

1 0 8 . 5 1 0 8 . 6 1 0 8 . 7 1 0 8 . 8 1 0 8 . 9

1 0 9 . o 1 0 9 . 1 1 0 9 . 2 1 0 9 . 3 1 0 9 . 4

1 0 9 . 5 1 0 9 . 6 1 0 9 . 7 1 0 9 . 8 1 0 9 . 9

110. o

O . 9 8 1 9 3 O . 9 8 1 8 9 O . 9 8 1 8 5 O . 9 8 1 8 1 O . 9 8 1 7 7

O . 9 8 1 7 3 O . 9 8 1 6 9 O . 9 8 1 6 4 O . 9 8 1 6 0 O . 9 8 1 5 6

O . 9 8 1 5 2 O . 9 8 1 4 8 O . 9 8 1 4 4 O . 9 8 1 4 0 O . 9 8 1 3 6

O . 9 8 1 3 2 O . 9 8 1 2 8 O . 9 8 1 2 4 O . 9 8 1 2 0 0 . 9 8 1 1 6

O . 9 8 1 1 2 O . 9 8 1 0 8 O . 9 8 1 0 4 O . 9 8 1 0 0 O . 9 8 0 9 6

O . 9 8 0 9 2 O . 9 8 0 8 8 O . 9 8 0 8 4 O . 9 8 0 8 0 O . 9 8 0 7 6

O . 9 8 0 7 2 O . 9 8 0 6 8 O . 9 8 0 6 4 O . 9 8 0 5 9 O . 9 8 0 5 5

O . 9 8 0 5 1 O . 9 8 0 4 7 O . 9 8 0 4 3 O . 9 8 0 3 9 O . 9 8 0 3 5

O . 9 8 0 3 1 O . 9 8 0 2 7 O . 9 8 0 2 3 O . 9 8 0 1 9 O . 9 8 0 1 5

O . 9 8 0 1 1 O . 9 8 0 0 7 O . 9 8 0 0 3 0 . 9 7 9 9 9 0 . 9 7 9 9 5

0 . 9 7 9 9 1

O . 9 8 1 9 3 O . 9 8 1 8 9 O . 9 8 1 8 5 O . 9 8 1 8 1 O . 9 8 1 7 7

O . 9 8 1 7 3 O . 9 8 1 6 9 O . 9 8 1 6 5 O . 9 8 1 6 1 O . 9 8 1 5 7

O . 9 8 1 5 3 0 . 9 8 1 4 9 O . 9 8 1 4 5 O . 9 8 1 4 1 O . 9 8 1 3 7

O . 9 8 1 3 3 O . 9 8 1 2 9 O . 9 8 1 2 5 O . 9 8 1 2 0 0 . 9 8 1 1 6

O . 9 8 1 1 2 O . 9 8 1 0 8 O . 9 8 1 0 4 O . 9 8 1 0 0 O . 9 8 0 9 6

O . 9 8 0 9 2 O . 9 8 0 8 8 O . 9 8 0 8 4 O . 9 8 0 8 0 O . 9 8 0 7 6

O . 9 8 0 7 2 O . 9 8 0 6 8 O . 9 8 0 6 4 O . 9 8 0 6 0 O . 9 8 0 5 6

O . 9 8 0 5 2 O . 9 8 0 4 8 O . 9 8 0 4 4 O . 9 8 0 4 0 O . 9 8 0 3 6

O . 9 8 0 3 2 O . 9 8 0 2 8 O . 9 8 0 2 4 O . 9 8 0 2 0 O . 9 8 0 1 5

O . 9 8 0 1 1 O . 9 8 0 0 7 O . 9 8 0 0 3 0 . 9 7 9 9 9 0 . 9 7 9 9 5

0 . 9 7 9 9 1

O . 9 8 1 9 4 O . 9 8 1 8 9 O . 9 8 1 8 5 O . 9 8 1 8 1 O . 9 8 1 7 7

O . 9 8 1 7 3 O . 9 8 1 6 9 O . 9 8 1 6 5 O . 9 8 1 6 1 O . 9 8 1 5 7

O . 9 8 1 5 3 0 . 9 8 1 4 9 O . 9 8 1 4 5 O . 9 8 1 4 1 O . 9 8 1 3 7

O . 9 8 1 3 3 O . 9 8 1 2 9 O . 9 8 1 2 5 O . 9 8 1 2 1 O . 9 8 1 1 7

O . 9 8 1 1 3 O . 9 8 1 0 9 O . 9 8 1 0 5 O . 9 8 1 0 1 O . 9 8 0 9 7

O . 9 8 0 9 3 O . 9 8 0 8 9 O . 9 8 0 8 5 O . 9 8 0 8 1 O . 9 8 0 7 6

O . 9 8 0 7 2 O . 9 8 0 6 8 O . 9 8 0 6 4 O . 9 8 0 6 0 O . 9 8 0 5 6

O . 9 8 0 5 2 O . 9 8 0 4 8 O . 9 8 0 4 4 O . 9 8 0 4 0 O . 9 8 0 3 6

O . 9 8 0 3 2 O . 9 8 0 2 8 O . 9 8 0 2 4 O . 9 8 0 2 0 O . 9 8 0 1 6

O . 9 8 0 1 2 O . 9 8 0 0 8 O . 9 8 0 0 4 O . 9 8 0 0 0 0 . 9 7 9 9 6

0 . 9 7 9 9 2

O . 9 8 1 9 4 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 2 O . 9 8 1 7 8

O . 9 8 1 7 4 O . 9 8 1 7 0 O . 9 8 1 6 6 0 . 9 8 1 6 2 O . 9 8 1 5 8

O . 9 8 1 5 4 O . 9 8 1 5 0 0 . 9 8 1 4 6 O . 9 8 1 4 1 O . 9 8 1 3 7

O . 9 8 1 3 3 O . 9 8 1 2 9 O . 9 8 1 2 5 O . 9 8 1 2 1 O . 9 8 1 1 7

O . 9 8 1 1 3 O . 9 8 1 0 9 O . 9 8 1 0 5 O . 9 8 1 0 1 O . 9 8 0 9 7

O . 9 8 0 9 3 O . 9 8 0 8 9 O . 9 8 0 8 5 O . 9 8 0 8 1 O . 9 8 0 7 7

O . 9 8 0 7 3 O . 9 8 0 6 9 O . 9 8 0 6 5 O . 9 8 0 6 1 O . 9 8 0 5 7

O . 9 8 0 5 3 O . 9 8 0 4 9 O . 9 8 0 4 5 O . 9 8 0 4 1 O . 9 8 0 3 7

O . 9 8 0 3 3 O . 9 8 0 2 8 O . 9 8 0 2 4 O . 9 8 0 2 0 O . 9 8 0 1 6

O . 9 8 0 1 2 O . 9 8 0 0 8 O . 9 8 0 0 4 O . 9 8 0 0 0 0 . 9 7 9 9 6

0 . 9 7 9 9 2

O . 9 8 1 9 4 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 2 O . 9 8 1 7 8

O . 9 8 1 7 4 O . 9 8 1 7 0 O . 9 8 1 6 6 0 . 9 8 1 6 2 O . 9 8 1 5 8

O . 9 8 1 5 4 O . 9 8 1 5 0 0 . 9 8 1 4 6 O . 9 8 1 4 2 O . 9 8 1 3 8

O . 9 8 1 3 4 O . 9 8 1 3 0 O . 9 8 1 2 6 O . 9 8 1 2 2 O . 9 8 1 1 8

O . 9 8 1 1 4 O . 9 8 1 1 0 O . 9 8 1 0 6 O . 9 8 1 0 2 O . 9 8 0 9 7

O . 9 8 0 9 3 O . 9 8 0 8 9 O . 9 8 0 8 5 O . 9 8 0 8 1 O . 9 8 0 7 7

O . 9 8 0 7 3 O . 9 8 0 6 9 O . 9 8 0 6 5 O . 9 8 0 6 1 O . 9 8 0 5 7

O . 9 8 0 5 3 O . 9 8 0 4 9 O . 9 8 0 4 5 O . 9 8 0 4 1 O . 9 8 0 3 7

O . 9 8 0 3 3 O . 9 8 0 2 9 O . 9 8 0 2 5 O . 9 8 0 2 1 O . 9 8 0 1 7

O . 9 8 0 1 3 O . 9 8 0 0 9 O . 9 8 0 0 5 O . 9 8 0 0 1 0 . 9 7 9 9 7

0 . 9 7 9 9 3

O . 9 8 1 9 5 O . 9 8 1 9 1 O . 9 8 1 8 7 O . 9 8 1 8 3 0 . 9 8 1 7 9

O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 6 0 . 9 8 1 6 2 O . 9 8 1 5 8

O . 9 8 1 5 4 O . 9 8 1 5 0 0 . 9 8 1 4 6 O . 9 8 1 4 2 O . 9 8 1 3 8

O . 9 8 1 3 4 O . 9 8 1 3 0 O . 9 8 1 2 6 O . 9 8 1 2 2 O . 9 8 1 1 8

O . 9 8 1 1 4 O . 9 8 1 1 0 O . 9 8 1 0 6 O . 9 8 1 0 2 O . 9 8 0 9 8

O . 9 8 0 9 4 O . 9 8 0 9 0 O . 9 8 0 8 6 O . 9 8 0 8 2 O . 9 8 0 7 8

O . 9 8 0 7 4 O . 9 8 0 7 0 O . 9 8 0 6 6 O . 9 8 0 6 2 O . 9 8 0 5 8

O . 9 8 0 5 4 O . 9 8 0 5 0 O . 9 8 0 4 5 O . 9 8 0 4 1 O . 9 8 0 3 7

O . 9 8 0 3 3 O . 9 8 0 2 9 O . 9 8 0 2 5 O . 9 8 0 2 1 O . 9 8 0 1 7

O . 9 8 0 1 3 O . 9 8 0 0 9 O . 9 8 0 0 5 O . 9 8 0 0 1 0 . 9 7 9 9 7

0 . 9 7 9 9 3

O . 9 8 1 9 5 O . 9 8 1 9 1 O . 9 8 1 8 7 O . 9 8 1 8 3 0 . 9 8 1 7 9

O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 7 O . 9 8 1 6 3 O . 9 8 1 5 9

O . 9 8 1 5 5 O . 9 8 1 5 1 O . 9 8 1 4 7 O . 9 8 1 4 3 O . 9 8 1 3 9

O . 9 8 1 3 5 O . 9 8 1 3 1 O . 9 8 1 2 7 O . 9 8 1 2 3 O . 9 8 1 1 8

O . 9 8 1 1 4 O . 9 8 1 1 0 O . 9 8 1 0 6 O . 9 8 1 0 2 O . 9 8 0 9 8

O . 9 8 0 9 4 O . 9 8 0 9 0 O . 9 8 0 8 6 O . 9 8 0 8 2 O . 9 8 0 7 8

O . 9 8 0 7 4 O . 9 8 0 7 0 O . 9 8 0 6 6 O . 9 8 0 6 2 O . 9 8 0 5 8

O . 9 8 0 5 4 O . 9 8 0 5 0 O . 9 8 0 4 6 O . 9 8 0 4 2 O . 9 8 0 3 8

O . 9 8 0 3 4 O . 9 8 0 3 0 O . 9 8 0 2 6 O . 9 8 0 2 2 O . 9 8 0 1 8

O . 9 8 0 1 4 O . 9 8 0 1 0 O . 9 8 0 0 6 O . 9 8 0 0 2 0 . 9 7 9 9 7

0 . 9 7 9 9 3

1 0 5 . O 1 0 5 . 1 1 0 5 . 2 1 0 5 . 3 1 0 5 . 4

1 0 5 . 5 1 0 5 . 6 1 0 5 . 7 1 0 5 . 8 1 0 5 . 9

1 0 6 . 0 1 0 6 . 1 1 0 6 . 2 1 0 6 . 3 1 0 6 . 4

1 0 6 . 5 1 0 6 . 6 1 0 6 . 7 1 0 6 . 8 1 0 6 . 9

1 0 7 . 0 1 0 7 . 1 1 0 7 . 2 1 0 7 . 3 1 0 7 . 4

1 0 7 . 5 1 0 7 . 6 1 0 7 . 7 1 0 7 . 8 1 0 7 . 9

1 0 8 . O 1 0 8 . 1 1 0 8 . 2 1 0 8 . 3 1 0 8 . 4

1 0 8 . 5 1 0 8 . 6 1 0 8 . 7 1 0 8 . 8 1 0 8 . 9

1 0 9 . o 1 0 9 . 1 1 0 9 . 2 1 0 9 . 3 1 0 9 . 4

1 0 9 . 5 1 0 9 . 6 1 0 9 . 7 1 0 9 . 8 1 0 9 . 9

110. o



--`,,`,,,-`-`,,`,,`,`,,`---


Table 24B. Volume Correction Factor Due to Temperature Against Relative Density at 60'F (Refined Products )




1 0 5 . O 1 0 5 . 1 1 0 5 . 2 1 0 5 . 3 1 0 5 . 4

1 0 5 . 5 1 0 5 . 6 1 0 5 . 7 1 0 5 . 8 1 0 5 . 9

1 0 6 . 0 1 0 6 . 1 1 0 6 . 2 1 0 6 . 3 1 0 6 . 4

1 0 6 . 5 1 0 6 . 6 1 0 6 . 7 1 0 6 . 8 1 0 6 . 9

1 0 7 . 0 1 0 7 . 1 1 0 7 . 2 1 0 7 . 3 1 0 7 . 4

1 0 7 . 5 1 0 7 . 6 1 0 7 . 7 1 0 7 . 8 1 0 7 . 9

1 0 8 . O 1 0 8 . 1 1 0 8 . 2 1 0 8 . 3 1 0 8 . 4

1 0 8 . 5 1 0 8 . 6 1 0 8 . 7 1 0 8 . 8 1 0 8 . 9

1 0 9 . o 1 0 9 . 1 1 0 9 . 2 1 0 9 . 3 1 0 9 . 4

1 0 9 . 5 1 0 9 . 6 1 0 9 . 7 1 0 9 . 8 1 0 9 . 9

110. o

O . 9 8 1 2 7 O . 9 8 1 2 3 O . 9 8 1 1 8 O . 9 8 1 1 4 O . 9 8 1 1 0

O . 9 8 1 0 6 O . 9 8 1 0 2 O . 9 8 0 9 8 O . 9 8 0 9 3 O . 9 8 0 8 9

O . 9 8 0 8 5 O . 9 8 0 8 1 O . 9 8 0 7 7 O . 9 8 0 7 2 O . 9 8 0 6 8

O . 9 8 0 6 4 O . 9 8 0 6 0 O . 9 8 0 5 6 O . 9 8 0 5 2 O . 9 8 0 4 7

O . 9 8 0 4 3 O . 9 8 0 3 9 O . 9 8 0 3 5 O . 9 8 0 3 1 O . 9 8 0 2 6

O . 9 8 0 2 2 O . 9 8 0 1 8 O . 9 8 0 1 4 O . 9 8 0 1 0 O . 9 8 0 0 5

O . 9 8 0 0 1 0 . 9 7 9 9 7 0 . 9 7 9 9 3 0 . 9 7 9 8 9 O . 9 7 9 8 5

O . 9 7 9 8 0 0 . 9 7 9 7 6 O . 9 7 9 7 2 0 . 9 7 9 6 8 0 . 9 7 9 6 4

0 . 9 7 9 5 9 O . 9 7 9 5 5 O . 9 7 9 5 1 0 . 9 7 9 4 7 0 . 9 7 9 4 3

O . 9 7 9 3 8 O . 9 7 9 3 4 O . 9 7 9 3 0 0 . 9 7 9 2 6 O . 9 7 9 2 2

0 . 9 7 9 1 8

O . 9 8 1 2 7 O . 9 8 1 2 3 0 . 9 8 1 1 9 O . 9 8 1 1 5 O . 9 8 1 1 0

O . 9 8 1 0 6 O . 9 8 1 0 2 O . 9 8 0 9 8 O . 9 8 0 9 4 O . 9 8 0 8 9

O . 9 8 0 8 5 O . 9 8 0 8 1 O . 9 8 0 7 7 O . 9 8 0 7 3 O . 9 8 0 6 9

O . 9 8 0 6 4 O . 9 8 0 6 0 O . 9 8 0 5 6 O . 9 8 0 5 2 O . 9 8 0 4 8

O . 9 8 0 4 3 O . 9 8 0 3 9 O . 9 8 0 3 5 O . 9 8 0 3 1 O . 9 8 0 2 7

O . 9 8 0 2 2 O . 9 8 0 1 8 O . 9 8 0 1 4 O . 9 8 0 1 0 O . 9 8 0 0 6

O . 9 8 0 0 2 0 . 9 7 9 9 7 0 . 9 7 9 9 3 0 . 9 7 9 8 9 O . 9 7 9 8 5

O . 9 7 9 8 1 0 . 9 7 9 7 6 O . 9 7 9 7 2 0 . 9 7 9 6 8 0 . 9 7 9 6 4

0 . 9 7 9 6 0 0 . 9 7 9 5 6 O . 9 7 9 5 1 0 . 9 7 9 4 7 0 . 9 7 9 4 3

0 . 9 7 9 3 9 O . 9 7 9 3 5 O . 9 7 9 3 0 0 . 9 7 9 2 6 O . 9 7 9 2 2

0 . 9 7 9 1 8

O . 9 8 1 2 7 O . 9 8 1 2 3 0 . 9 8 1 1 9 O . 9 8 1 1 5 O . 9 8 1 1 1

O . 9 8 1 0 6 O . 9 8 1 0 2 O . 9 8 0 9 8 O . 9 8 0 9 4 O . 9 8 0 9 0

O . 9 8 0 8 6 O . 9 8 0 8 1 O . 9 8 0 7 7 O . 9 8 0 7 3 O . 9 8 0 6 9

O . 9 8 0 6 5 O . 9 8 0 6 0 O . 9 8 0 5 6 O . 9 8 0 5 2 O . 9 8 0 4 8

O . 9 8 0 4 4 O . 9 8 0 4 0 O . 9 8 0 3 5 O . 9 8 0 3 1 O . 9 8 0 2 7

O . 9 8 0 2 3 O . 9 8 0 1 9 O . 9 8 0 1 4 O . 9 8 0 1 0 O . 9 8 0 0 6

O . 9 8 0 0 2 0 . 9 7 9 9 8 0 . 9 7 9 9 3 0 . 9 7 9 8 9 O . 9 7 9 8 5

O . 9 7 9 8 1 0 . 9 7 9 7 7 0 . 9 7 9 7 3 0 . 9 7 9 6 8 0 . 9 7 9 6 4

0 . 9 7 9 6 0 0 . 9 7 9 5 6 O . 9 7 9 5 2 0 . 9 7 9 4 7 0 . 9 7 9 4 3

0 . 9 7 9 3 9 O . 9 7 9 3 5 O . 9 7 9 3 1 0 . 9 7 9 2 6 O . 9 7 9 2 2

0 . 9 7 9 1 8

O . 9 8 1 2 8 O . 9 8 1 2 3 0 . 9 8 1 1 9 O . 9 8 1 1 5 O . 9 8 1 1 1

O . 9 8 1 0 7 O . 9 8 1 0 3 O . 9 8 0 9 8 O . 9 8 0 9 4 O . 9 8 0 9 0

O . 9 8 0 8 6 O . 9 8 0 8 2 O . 9 8 0 7 7 O . 9 8 0 7 3 O . 9 8 0 6 9

O . 9 8 0 6 5 O . 9 8 0 6 1 O . 9 8 0 5 7 O . 9 8 0 5 2 O . 9 8 0 4 8

O . 9 8 0 4 4 O . 9 8 0 4 0 O . 9 8 0 3 6 O . 9 8 0 3 1 O . 9 8 0 2 7

O . 9 8 0 2 3 O . 9 8 0 1 9 O . 9 8 0 1 5 O . 9 8 0 1 0 O . 9 8 0 0 6

O . 9 8 0 0 2 0 . 9 7 9 9 8 0 . 9 7 9 9 4 0 . 9 7 9 9 0 O . 9 7 9 8 5

O . 9 7 9 8 1 0 . 9 7 9 7 7 0 . 9 7 9 7 3 0 . 9 7 9 6 9 0 . 9 7 9 6 4

0 . 9 7 9 6 0 0 . 9 7 9 5 6 O . 9 7 9 5 2 0 . 9 7 9 4 8 0 . 9 7 9 4 4

0 . 9 7 9 3 9 O . 9 7 9 3 5 O . 9 7 9 3 1 0 . 9 7 9 2 7 0 . 9 7 9 2 3

0 . 9 7 9 1 8

O . 9 8 1 2 8 O . 9 8 1 2 4 O . 9 8 1 2 0 O . 9 8 1 1 5 O . 9 8 1 1 1

O . 9 8 1 0 7 O . 9 8 1 0 3 O . 9 8 0 9 9 O . 9 8 0 9 4 O . 9 8 0 9 0

O . 9 8 0 8 6 O . 9 8 0 8 2 O . 9 8 0 7 8 O . 9 8 0 7 4 O . 9 8 0 6 9

O . 9 8 0 6 5 O . 9 8 0 6 1 O . 9 8 0 5 7 O . 9 8 0 5 3 O . 9 8 0 4 8

O . 9 8 0 4 4 O . 9 8 0 4 0 O . 9 8 0 3 6 O . 9 8 0 3 2 O . 9 8 0 2 8

O . 9 8 0 2 3 O . 9 8 0 1 9 O . 9 8 0 1 5 O . 9 8 0 1 1 O . 9 8 0 0 7

O . 9 8 0 0 2 0 . 9 7 9 9 8 0 . 9 7 9 9 4 0 . 9 7 9 9 0 0 . 9 7 9 8 6

O . 9 7 9 8 1 0 . 9 7 9 7 7 0 . 9 7 9 7 3 0 . 9 7 9 6 9 0 . 9 7 9 6 5

0 . 9 7 9 6 1 0 . 9 7 9 5 6 O . 9 7 9 5 2 0 . 9 7 9 4 8 0 . 9 7 9 4 4

0 . 9 7 9 4 0 O . 9 7 9 3 5 O . 9 7 9 3 1 0 . 9 7 9 2 7 0 . 9 7 9 2 3

0 . 9 7 9 1 9

O . 9 8 1 2 8 O . 9 8 1 2 4 O . 9 8 1 2 0 0 . 9 8 1 1 6 O . 9 8 1 1 1

O . 9 8 1 0 7 O . 9 8 1 0 3 O . 9 8 0 9 9 O . 9 8 0 9 5 O . 9 8 0 9 1

O . 9 8 0 8 6 O . 9 8 0 8 2 O . 9 8 0 7 8 O . 9 8 0 7 4 O . 9 8 0 7 0

O . 9 8 0 6 5 O . 9 8 0 6 1 O . 9 8 0 5 7 O . 9 8 0 5 3 O . 9 8 0 4 9

O . 9 8 0 4 5 O . 9 8 0 4 0 O . 9 8 0 3 6 O . 9 8 0 3 2 O . 9 8 0 2 8

O . 9 8 0 2 4 O . 9 8 0 1 9 O . 9 8 0 1 5 O . 9 8 0 1 1 O . 9 8 0 0 7

O . 9 8 0 0 3 0 . 9 7 9 9 9 0 . 9 7 9 9 4 0 . 9 7 9 9 0 0 . 9 7 9 8 6

O . 9 7 9 8 2 0 . 9 7 9 7 8 0 . 9 7 9 7 3 0 . 9 7 9 6 9 0 . 9 7 9 6 5

0 . 9 7 9 6 1 O . 9 7 9 5 7 O . 9 7 9 5 2 0 . 9 7 9 4 8 0 . 9 7 9 4 4

0 . 9 7 9 4 0 0 . 9 7 9 3 6 O . 9 7 9 3 2 0 . 9 7 9 2 7 0 . 9 7 9 2 3

0 . 9 7 9 1 9

O . 9 8 1 2 8 O . 9 8 1 2 4 O . 9 8 1 2 0 0 . 9 8 1 1 6 O . 9 8 1 1 2

O . 9 8 1 0 8 O . 9 8 1 0 3 O . 9 8 0 9 9 O . 9 8 0 9 5 O . 9 8 0 9 1

O . 9 8 0 8 7 O . 9 8 0 8 2 O . 9 8 0 7 8 O . 9 8 0 7 4 O . 9 8 0 7 0

O . 9 8 0 6 6 O . 9 8 0 6 2 O . 9 8 0 5 7 O . 9 8 0 5 3 O . 9 8 0 4 9

O . 9 8 0 4 5 O . 9 8 0 4 1 O . 9 8 0 3 6 O . 9 8 0 3 2 O . 9 8 0 2 8

O . 9 8 0 2 4 O . 9 8 0 2 0 O . 9 8 0 1 6 O . 9 8 0 1 1 O . 9 8 0 0 7

O . 9 8 0 0 3 0 . 9 7 9 9 9 0 . 9 7 9 9 5 0 . 9 7 9 9 0 0 . 9 7 9 8 6

O . 9 7 9 8 2 0 . 9 7 9 7 8 0 . 9 7 9 7 4 0 . 9 7 9 6 9 0 . 9 7 9 6 5

0 . 9 7 9 6 1 O . 9 7 9 5 7 O . 9 7 9 5 3 0 . 9 7 9 4 9 0 . 9 7 9 4 4

0 . 9 7 9 4 0 0 . 9 7 9 3 6 O . 9 7 9 3 2 0 . 9 7 9 2 8 0 . 9 7 9 2 3

0 . 9 7 9 1 9

1 0 5 . O 1 0 5 . 1 1 0 5 . 2 1 0 5 . 3 1 0 5 . 4

1 0 5 . 5 1 0 5 . 6 1 0 5 . 7 1 0 5 . 8 1 0 5 . 9

1 0 6 . 0 1 0 6 . 1 1 0 6 . 2 1 0 6 . 3 1 0 6 . 4

1 0 6 . 5 1 0 6 . 6 1 0 6 . 7 1 0 6 . 8 1 0 6 . 9

1 0 7 . 0 1 0 7 . 1 1 0 7 . 2 1 0 7 . 3 1 0 7 . 4

1 0 7 . 5 1 0 7 . 6 1 0 7 . 7 1 0 7 . 8 1 0 7 . 9

1 0 8 . O 1 0 8 . 1 1 0 8 . 2 1 0 8 . 3 1 0 8 . 4

1 0 8 . 5 1 0 8 . 6 1 0 8 . 7 1 0 8 . 8 1 0 8 . 9

1 0 9 . o 1 0 9 . 1 1 0 9 . 2 1 0 9 . 3 1 0 9 . 4

1 0 9 . 5 1 0 9 . 6 1 0 9 . 7 1 0 9 . 8 1 0 9 . 9

110. o



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.10 Instructions to Generate Table 24D - Correction of Volume to 60°F Against Specific Gravity 60/60”F for Generalized Lubricating Oils

Input Variables: Base relative density (60/60’F) and temperature. Pressure set to O psig.


Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:


Increment relative density (60/60’F) value by 0.0001 in range of 0.8017 to 1.1646. Ensure that the base relative density value remains rounded consistent with instructions in 1 1.1.5.4.

Increment temperature by 0.1’F in range of -58.0” to 302’F. Ensure that the temperature value remains rounded consistent with instructions in 1 1.1.5.4.


Determine the CTL value using procedure in 11.1.6.1 & speciqing commodity group “A” or “BD” as appropriate. Round the CTL value consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 24D. Volume Correction Factor Due to Temperature Against Relative Density at 60'F (lube Oils)




1 0 5 . O 1 0 5 . 1 1 0 5 . 2 1 0 5 . 3 1 0 5 . 4

1 0 5 . 5 1 0 5 . 6 1 0 5 . 7 1 0 5 . 8 1 0 5 . 9

1 0 6 . 0 1 0 6 . 1 1 0 6 . 2 1 0 6 . 3 1 0 6 . 4

1 0 6 . 5 1 0 6 . 6 1 0 6 . 7 1 0 6 . 8 1 0 6 . 9

1 0 7 . 0 1 0 7 . 1 1 0 7 . 2 1 0 7 . 3 1 0 7 . 4

1 0 7 . 5 1 0 7 . 6 1 0 7 . 7 1 0 7 . 8 1 0 7 . 9

1 0 8 . O 1 0 8 . 1 1 0 8 . 2 1 0 8 . 3 1 0 8 . 4

1 0 8 . 5 1 0 8 . 6 1 0 8 . 7 1 0 8 . 8 1 0 8 . 9

1 0 9 . o 1 0 9 . 1 1 0 9 . 2 1 0 9 . 3 1 0 9 . 4

1 0 9 . 5 1 0 9 . 6 1 0 9 . 7 1 0 9 . 8 1 0 9 . 9

110. o

O . 9 8 2 9 3 O . 9 8 2 8 9 O . 9 8 2 8 5 O . 9 8 2 8 1 O . 9 8 2 7 8

O . 9 8 2 7 4 O . 9 8 2 7 0 O . 9 8 2 6 6 0 . 9 8 2 6 2 O . 9 8 2 5 8

O . 9 8 2 5 5 O . 9 8 2 5 1 O . 9 8 2 4 7 O . 9 8 2 4 3 O . 9 8 2 3 9

O . 9 8 2 3 6 O . 9 8 2 3 2 O . 9 8 2 2 8 O . 9 8 2 2 4 O . 9 8 2 2 0

O . 9 8 2 1 7 O . 9 8 2 1 3 O . 9 8 2 0 9 O . 9 8 2 0 5 O . 9 8 2 0 1

O . 9 8 1 9 7 O . 9 8 1 9 4 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 2

O . 9 8 1 7 8 O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 7 O . 9 8 1 6 3

O . 9 8 1 5 9 O . 9 8 1 5 5 O . 9 8 1 5 2 O . 9 8 1 4 8 O . 9 8 1 4 4

O . 9 8 1 4 0 O . 9 8 1 3 6 O . 9 8 1 3 3 O . 9 8 1 2 9 O . 9 8 1 2 5

O . 9 8 1 2 1 O . 9 8 1 1 7 O . 9 8 1 1 4 O . 9 8 1 1 0 O . 9 8 1 0 6

O . 9 8 1 0 2

O . 9 8 2 9 3 O . 9 8 2 8 9 O . 9 8 2 8 5 O . 9 8 2 8 2 O . 9 8 2 7 8

O . 9 8 2 7 4 O . 9 8 2 7 0 O . 9 8 2 6 6 0 . 9 8 2 6 2 O . 9 8 2 5 9

O . 9 8 2 5 5 O . 9 8 2 5 1 O . 9 8 2 4 7 O . 9 8 2 4 3 O . 9 8 2 4 0

O . 9 8 2 3 6 O . 9 8 2 3 2 O . 9 8 2 2 8 O . 9 8 2 2 4 O . 9 8 2 2 1

O . 9 8 2 1 7 O . 9 8 2 1 3 O . 9 8 2 0 9 O . 9 8 2 0 5 O . 9 8 2 0 1

O . 9 8 1 9 8 O . 9 8 1 9 4 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 2

0 . 9 8 1 7 9 O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 7 O . 9 8 1 6 3

O . 9 8 1 6 0 O . 9 8 1 5 6 O . 9 8 1 5 2 O . 9 8 1 4 8 O . 9 8 1 4 4

O . 9 8 1 4 0 O . 9 8 1 3 7 O . 9 8 1 3 3 O . 9 8 1 2 9 O . 9 8 1 2 5

O . 9 8 1 2 1 O . 9 8 1 1 8 O . 9 8 1 1 4 O . 9 8 1 1 0 O . 9 8 1 0 6

O . 9 8 1 0 2

O . 9 8 2 9 3 O . 9 8 2 8 9 O . 9 8 2 8 6 O . 9 8 2 8 2 O . 9 8 2 7 8

O . 9 8 2 7 4 O . 9 8 2 7 0 O . 9 8 2 6 6 O . 9 8 2 6 3 O . 9 8 2 5 9

O . 9 8 2 5 5 O . 9 8 2 5 1 O . 9 8 2 4 7 O . 9 8 2 4 4 O . 9 8 2 4 0

O . 9 8 2 3 6 O . 9 8 2 3 2 O . 9 8 2 2 8 O . 9 8 2 2 5 O . 9 8 2 2 1

O . 9 8 2 1 7 O . 9 8 2 1 3 O . 9 8 2 0 9 O . 9 8 2 0 5 O . 9 8 2 0 2

O . 9 8 1 9 8 O . 9 8 1 9 4 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 3

0 . 9 8 1 7 9 O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 7 O . 9 8 1 6 4

O . 9 8 1 6 0 O . 9 8 1 5 6 O . 9 8 1 5 2 O . 9 8 1 4 8 O . 9 8 1 4 4

O . 9 8 1 4 1 O . 9 8 1 3 7 O . 9 8 1 3 3 O . 9 8 1 2 9 O . 9 8 1 2 5

O . 9 8 1 2 2 O . 9 8 1 1 8 O . 9 8 1 1 4 O . 9 8 1 1 0 O . 9 8 1 0 6

O . 9 8 1 0 2

O . 9 8 2 9 3 O . 9 8 2 9 0 O . 9 8 2 8 6 O . 9 8 2 8 2 O . 9 8 2 7 8

O . 9 8 2 7 4 O . 9 8 2 7 0 O . 9 8 2 6 7 O . 9 8 2 6 3 O . 9 8 2 5 9

O . 9 8 2 5 5 O . 9 8 2 5 1 O . 9 8 2 4 8 O . 9 8 2 4 4 O . 9 8 2 4 0

O . 9 8 2 3 6 O . 9 8 2 3 2 O . 9 8 2 2 9 O . 9 8 2 2 5 O . 9 8 2 2 1

O . 9 8 2 1 7 O . 9 8 2 1 3 O . 9 8 2 0 9 O . 9 8 2 0 6 O . 9 8 2 0 2

O . 9 8 1 9 8 O . 9 8 1 9 4 O . 9 8 1 9 0 O . 9 8 1 8 7 O . 9 8 1 8 3

0 . 9 8 1 7 9 O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 8 O . 9 8 1 6 4

O . 9 8 1 6 0 O . 9 8 1 5 6 O . 9 8 1 5 2 O . 9 8 1 4 8 O . 9 8 1 4 5

O . 9 8 1 4 1 O . 9 8 1 3 7 O . 9 8 1 3 3 O . 9 8 1 2 9 O . 9 8 1 2 6

O . 9 8 1 2 2 O . 9 8 1 1 8 O . 9 8 1 1 4 O . 9 8 1 1 0 O . 9 8 1 0 7

O . 9 8 1 0 3

O . 9 8 2 9 4 O . 9 8 2 9 0 O . 9 8 2 8 6 O . 9 8 2 8 2 O . 9 8 2 7 8

O . 9 8 2 7 4 O . 9 8 2 7 1 O . 9 8 2 6 7 O . 9 8 2 6 3 O . 9 8 2 5 9

O . 9 8 2 5 5 O . 9 8 2 5 2 O . 9 8 2 4 8 O . 9 8 2 4 4 O . 9 8 2 4 0

O . 9 8 2 3 6 O . 9 8 2 3 3 O . 9 8 2 2 9 O . 9 8 2 2 5 O . 9 8 2 2 1

O . 9 8 2 1 7 O . 9 8 2 1 3 O . 9 8 2 1 0 O . 9 8 2 0 6 O . 9 8 2 0 2

O . 9 8 1 9 8 O . 9 8 1 9 4 O . 9 8 1 9 1 O . 9 8 1 8 7 O . 9 8 1 8 3

0 . 9 8 1 7 9 O . 9 8 1 7 5 O . 9 8 1 7 2 O . 9 8 1 6 8 O . 9 8 1 6 4

O . 9 8 1 6 0 O . 9 8 1 5 6 O . 9 8 1 5 2 0 . 9 8 1 4 9 O . 9 8 1 4 5

O . 9 8 1 4 1 O . 9 8 1 3 7 O . 9 8 1 3 3 O . 9 8 1 3 0 O . 9 8 1 2 6

O . 9 8 1 2 2 O . 9 8 1 1 8 O . 9 8 1 1 4 O . 9 8 1 1 1 O . 9 8 1 0 7

O . 9 8 1 0 3

O . 9 8 2 9 4 O . 9 8 2 9 0 O . 9 8 2 8 6 O . 9 8 2 8 2 O . 9 8 2 7 8

O . 9 8 2 7 5 O . 9 8 2 7 1 O . 9 8 2 6 7 O . 9 8 2 6 3 O . 9 8 2 5 9

O . 9 8 2 5 6 O . 9 8 2 5 2 O . 9 8 2 4 8 O . 9 8 2 4 4 O . 9 8 2 4 0

O . 9 8 2 3 7 O . 9 8 2 3 3 O . 9 8 2 2 9 O . 9 8 2 2 5 O . 9 8 2 2 1

O . 9 8 2 1 7 O . 9 8 2 1 4 O . 9 8 2 1 0 O . 9 8 2 0 6 O . 9 8 2 0 2

O . 9 8 1 9 8 O . 9 8 1 9 5 O . 9 8 1 9 1 O . 9 8 1 8 7 O . 9 8 1 8 3

0 . 9 8 1 7 9 0 . 9 8 1 7 6 O . 9 8 1 7 2 O . 9 8 1 6 8 O . 9 8 1 6 4

O . 9 8 1 6 0 O . 9 8 1 5 6 O . 9 8 1 5 3 0 . 9 8 1 4 9 O . 9 8 1 4 5

O . 9 8 1 4 1 O . 9 8 1 3 7 O . 9 8 1 3 4 O . 9 8 1 3 0 O . 9 8 1 2 6

O . 9 8 1 2 2 O . 9 8 1 1 8 O . 9 8 1 1 5 O . 9 8 1 1 1 O . 9 8 1 0 7

O . 9 8 1 0 3

O . 9 8 2 9 4 O . 9 8 2 9 0 O . 9 8 2 8 6 O . 9 8 2 8 2 0 . 9 8 2 7 9

O . 9 8 2 7 5 O . 9 8 2 7 1 O . 9 8 2 6 7 O . 9 8 2 6 3 O . 9 8 2 6 0

O . 9 8 2 5 6 O . 9 8 2 5 2 O . 9 8 2 4 8 O . 9 8 2 4 4 O . 9 8 2 4 1

O . 9 8 2 3 7 O . 9 8 2 3 3 O . 9 8 2 2 9 O . 9 8 2 2 5 O . 9 8 2 2 1

O . 9 8 2 1 8 O . 9 8 2 1 4 O . 9 8 2 1 0 O . 9 8 2 0 6 O . 9 8 2 0 2

0 . 9 8 1 9 9 O . 9 8 1 9 5 O . 9 8 1 9 1 O . 9 8 1 8 7 O . 9 8 1 8 3

O . 9 8 1 8 0 0 . 9 8 1 7 6 O . 9 8 1 7 2 O . 9 8 1 6 8 O . 9 8 1 6 4

O . 9 8 1 6 1 O . 9 8 1 5 7 O . 9 8 1 5 3 0 . 9 8 1 4 9 O . 9 8 1 4 5

O . 9 8 1 4 1 O . 9 8 1 3 8 O . 9 8 1 3 4 O . 9 8 1 3 0 O . 9 8 1 2 6

O . 9 8 1 2 2 0 . 9 8 1 1 9 O . 9 8 1 1 5 O . 9 8 1 1 1 O . 9 8 1 0 7

O . 9 8 1 0 3

1 0 5 . O 1 0 5 . 1 1 0 5 . 2 1 0 5 . 3 1 0 5 . 4

1 0 5 . 5 1 0 5 . 6 1 0 5 . 7 1 0 5 . 8 1 0 5 . 9

1 0 6 . 0 1 0 6 . 1 1 0 6 . 2 1 0 6 . 3 1 0 6 . 4

1 0 6 . 5 1 0 6 . 6 1 0 6 . 7 1 0 6 . 8 1 0 6 . 9

1 0 7 . 0 1 0 7 . 1 1 0 7 . 2 1 0 7 . 3 1 0 7 . 4

1 0 7 . 5 1 0 7 . 6 1 0 7 . 7 1 0 7 . 8 1 0 7 . 9

1 0 8 . O 1 0 8 . 1 1 0 8 . 2 1 0 8 . 3 1 0 8 . 4

1 0 8 . 5 1 0 8 . 6 1 0 8 . 7 1 0 8 . 8 1 0 8 . 9

1 0 9 . o 1 0 9 . 1 1 0 9 . 2 1 0 9 . 3 1 0 9 . 4

1 0 9 . 5 1 0 9 . 6 1 0 9 . 7 1 0 9 . 8 1 0 9 . 9

110. o



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.11 Instructions to Generate Table 53A - Correction of Observed Density to Density at 15°C for Generalized Crude Oils

Input Variables: Observed density and temperature. Pressure set to O Wa.

Output Variables: Base density at 15’C and O Wa (gauge).

Step 1: Hold pressure value at O Wa.

Step 2: Increment density value by 0.1 kg/m3 in range of 470.6 to 1197.7 kg/m3. Ensure that the density value remains rounded consistent with instructions in 11.1.5.4.

Step 3: Increment temperature by 0.05’C in range of -50.00’ to 150.00’C. Ensure that the temperature value remains rounded consistent with instructions in 11.1.5.4.

Step 4: Determine the base density using procedure in 11.1.7.2 & specimng commodity group “A.” Round the resulting density value for display consistent with instructions in 1 1.1.5.4.

Step 5: Increment the value of the density or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of density and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


Table 53A. Correction of Observed Density to 15'C Base Density (Crude Oils) If hydrometer used to determine density, apply glass correction before entering table

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 35.15 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 35.35 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 35.55 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 35.85 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0

Observed Pressure is O kPa (gauge)

Observed Density (kg/m3) 8 2 7 . 0 8 2 7 . 1 827 .2 8 2 7 . 3 827 .4 8 2 7 . 5 8 2 7 . 6

Corresponding Density at 15'C & O kPa (gauge), kg/m3

841.7 841 .7 841 .7 8 4 1 . 8 8 4 1 . 8

8 4 1 . 9 8 4 1 . 9 8 4 1 . 9 8 4 2 . O 8 4 2 . O

8 4 2 . O 8 4 2 . 1 8 4 2 . 1 8 4 2 . 1 842 .2

842 .2 842 .2 8 4 2 . 3 8 4 2 . 3 842 .4

842 .4 842 .4 8 4 2 . 5 8 4 2 . 5 8 4 2 . 5

8 4 2 . 6 8 4 2 . 6 8 4 2 . 6 842 .7 842 .7

8 4 2 . 8 8 4 2 . 8 8 4 2 . 8 8 4 2 . 9 8 4 2 . 9

8 4 2 . 9 8 4 3 . O 8 4 3 . O 8 4 3 . O 8 4 3 . 1

8 4 3 . 1 843 .2 843 .2 843 .2 8 4 3 . 3

8 4 3 . 3 8 4 3 . 3 843 .4 843 .4 843 .4

8 4 3 . 5

8 4 1 . 8 8 4 1 . 8 8 4 1 . 8 8 4 1 . 9 8 4 1 . 9

8 4 1 . 9 8 4 2 . O 8 4 2 . O 8 4 2 . 1 8 4 2 . 1

8 4 2 . 1 842 .2 842 .2 842 .2 8 4 2 . 3

8 4 2 . 3 8 4 2 . 3 842 .4 842 .4 8 4 2 . 5

8 4 2 . 5 8 4 2 . 5 8 4 2 . 6 8 4 2 . 6 8 4 2 . 6

842 .7 842 .7 842 .7 8 4 2 . 8 8 4 2 . 8

8 4 2 . 9 8 4 2 . 9 8 4 2 . 9 8 4 3 . O 8 4 3 . O

8 4 3 . O 8 4 3 . 1 8 4 3 . 1 8 4 3 . 1 843 .2

843 .2 8 4 3 . 3 8 4 3 . 3 8 4 3 . 3 843 .4

843 .4 843 .4 8 4 3 . 5 8 4 3 . 5 8 4 3 . 5

8 4 3 . 6

8 4 1 . 9 8 4 1 . 9 8 4 1 . 9 8 4 2 . O 8 4 2 . O

8 4 2 . O 8 4 2 . 1 8 4 2 . 1 842 .2 842 .2

842 .2 8 4 2 . 3 8 4 2 . 3 8 4 2 . 3 842 .4

842 .4 842 .4 8 4 2 . 5 8 4 2 . 5 8 4 2 . 6

8 4 2 . 6 8 4 2 . 6 842 .7 842 .7 842 .7

8 4 2 . 8 8 4 2 . 8 8 4 2 . 8 8 4 2 . 9 8 4 2 . 9

8 4 3 . O 8 4 3 . O 8 4 3 . O 8 4 3 . 1 8 4 3 . 1

8 4 3 . 1 843 .2 843 .2 843 .2 8 4 3 . 3

8 4 3 . 3 8 4 3 . 3 843 .4 843 .4 8 4 3 . 5

8 4 3 . 5 8 4 3 . 5 8 4 3 . 6 8 4 3 . 6 8 4 3 . 6

843 .7

8 4 2 . O 8 4 2 . O 8 4 2 . O 8 4 2 . 1 8 4 2 . 1

8 4 2 . 1 842 .2 842 .2 8 4 2 . 3 8 4 2 . 3

8 4 2 . 3 842 .4 842 .4 842 .4 8 4 2 . 5

8 4 2 . 5 8 4 2 . 5 8 4 2 . 6 8 4 2 . 6 842 .7

842 .7 842 .7 8 4 2 . 8 8 4 2 . 8 8 4 2 . 8

8 4 2 . 9 8 4 2 . 9 8 4 2 . 9 8 4 3 . O 8 4 3 . O

8 4 3 . O 8 4 3 . 1 8 4 3 . 1 843 .2 843 .2

843 .2 8 4 3 . 3 8 4 3 . 3 8 4 3 . 3 843 .4

843 .4 843 .4 8 4 3 . 5 8 4 3 . 5 8 4 3 . 6

8 4 3 . 6 8 4 3 . 6 843 .7 843 .7 843 .7

8 4 3 . 8

8 4 2 . 1 8 4 2 . 1 8 4 2 . 1 842 .2 842 .2

842 .2 8 4 2 . 3 8 4 2 . 3 842 .4 842 .4

842 .4 8 4 2 . 5 8 4 2 . 5 8 4 2 . 5 8 4 2 . 6

8 4 2 . 6 8 4 2 . 6 842 .7 842 .7 842 .7

8 4 2 . 8 8 4 2 . 8 8 4 2 . 9 8 4 2 . 9 8 4 2 . 9

8 4 3 . O 8 4 3 . O 8 4 3 . O 8 4 3 . 1 8 4 3 . 1

8 4 3 . 1 843 .2 843 .2 8 4 3 . 3 8 4 3 . 3

8 4 3 . 3 843 .4 843 .4 843 .4 8 4 3 . 5

8 4 3 . 5 8 4 3 . 5 8 4 3 . 6 8 4 3 . 6 843 .7

843 .7 843 .7 8 4 3 . 8 8 4 3 . 8 8 4 3 . 8

8 4 3 . 9

842 .2 842 .2 842 .2 8 4 2 . 3 8 4 2 . 3

8 4 2 . 3 842 .4 842 .4 8 4 2 . 5 8 4 2 . 5

8 4 2 . 5 8 4 2 . 6 8 4 2 . 6 8 4 2 . 6 842 .7

842 .7 842 .7 8 4 2 . 8 8 4 2 . 8 8 4 2 . 8

8 4 2 . 9 8 4 2 . 9 8 4 3 . O 8 4 3 . O 8 4 3 . O

8 4 3 . 1 8 4 3 . 1 8 4 3 . 1 843 .2 843 .2

843 .2 8 4 3 . 3 8 4 3 . 3 843 .4 843 .4

843 .4 8 4 3 . 5 8 4 3 . 5 8 4 3 . 5 8 4 3 . 6

8 4 3 . 6 8 4 3 . 6 843 .7 843 .7 8 4 3 . 8

8 4 3 . 8 8 4 3 . 8 8 4 3 . 9 8 4 3 . 9 8 4 3 . 9

8 4 4 . 0

8 4 2 . 3 8 4 2 . 3 8 4 2 . 3 842 .4 842 .4

842 .4 8 4 2 . 5 8 4 2 . 5 8 4 2 . 5 8 4 2 . 6

8 4 2 . 6 842 .7 842 .7 842 .7 8 4 2 . 8

8 4 2 . 8 8 4 2 . 8 8 4 2 . 9 8 4 2 . 9 8 4 2 . 9

8 4 3 . O 8 4 3 . O 8 4 3 . 1 8 4 3 . 1 8 4 3 . 1

843 .2 843 .2 843 .2 8 4 3 . 3 8 4 3 . 3

8 4 3 . 3 843 .4 843 .4 8 4 3 . 5 8 4 3 . 5

8 4 3 . 5 8 4 3 . 6 8 4 3 . 6 8 4 3 . 6 843 .7

843 .7 843 .7 8 4 3 . 8 8 4 3 . 8 8 4 3 . 8

8 4 3 . 9 8 4 3 . 9 8 4 4 . 0 8 4 4 . 0 8 4 4 . 0

8 4 4 . 1

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 35.15 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 35.35 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 35.55 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 35.85 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.12 Instructions to Generate Table 53B - Correction of Observed Density to Density at 15°C for Generalized Products


Output Variables: Base density at 15'C and O Wa (gauge).

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Hold pressure value at O Wa.

Increment density value by 0.1 kg/m3 in range of 470.5 to 1205.4 kg/m3. Ensure that the density value remains rounded consistent with instructions in 11.1.5.4.

Increment temperature by 0.05'C in range of -50.00' to 150.00'C. Ensure that the temperature value remains rounded consistent with instructions in 11.1.5.4.

Determine the base density using procedure in 11.1.7.2 & specimng commodity group "B." Round the resulting density value for display consistent with instructions in 1 1.1.5.4.

Increment the value of the density or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of density and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


Table 53B. Correction of Observed Density to 15'C Base Density (Refined Products) If hydrometer used to determine density, apply glass correction before entering table

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 3 5 . 1 5 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 3 5 . 3 5 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 3 5 . 5 5 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 3 5 . 8 5 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0


Observed Density (kg/m3) 8 2 7 . 0 8 2 7 . 1 8 2 7 . 2 8 2 7 . 3 8 2 7 . 4 8 2 7 . 5 8 2 7 . 6


8 4 1 . 2 8 4 1 . 3 8 4 1 . 3 8 4 1 . 3 8 4 1 . 4

8 4 1 . 4 8 4 1 . 5 8 4 1 . 5 8 4 1 . 5 8 4 1 . 6

8 4 1 . 6 8 4 1 . 6 8 4 1 . 7 8 4 1 . 7 8 4 1 . 7

8 4 1 . 8 8 4 1 . 8 8 4 1 . 8 8 4 1 . 9 8 4 1 . 9

8 4 2 . O 8 4 2 . O 8 4 2 . O 8 4 2 . 1 8 4 2 . 1

8 4 2 . 1 8 4 2 . 2 8 4 2 . 2 8 4 2 . 2 8 4 2 . 3

8 4 2 . 3 8 4 2 . 3 8 4 2 . 4 8 4 2 . 4 8 4 2 . 4

8 4 2 . 5 8 4 2 . 5 8 4 2 . 6 8 4 2 . 6 8 4 2 . 6

8 4 2 . 7 8 4 2 . 7 8 4 2 . 7 8 4 2 . 8 8 4 2 . 8

8 4 2 . 8 8 4 2 . 9 8 4 2 . 9 8 4 2 . 9 8 4 3 . O

8 4 3 . O

8 4 1 . 3 8 4 1 . 4 8 4 1 . 4 8 4 1 . 4 8 4 1 . 5

8 4 1 . 5 8 4 1 . 6 8 4 1 . 6 8 4 1 . 6 8 4 1 . 7

8 4 1 . 7 8 4 1 . 7 8 4 1 . 8 8 4 1 . 8 8 4 1 . 8

8 4 1 . 9 8 4 1 . 9 8 4 1 . 9 8 4 2 . O 8 4 2 . O

8 4 2 . 1 8 4 2 . 1 8 4 2 . 1 8 4 2 . 2 8 4 2 . 2

8 4 2 . 2 8 4 2 . 3 8 4 2 . 3 8 4 2 . 3 8 4 2 . 4

8 4 2 . 4 8 4 2 . 4 8 4 2 . 5 8 4 2 . 5 8 4 2 . 5

8 4 2 . 6 8 4 2 . 6 8 4 2 . 7 8 4 2 . 7 8 4 2 . 7

8 4 2 . 8 8 4 2 . 8 8 4 2 . 8 8 4 2 . 9 8 4 2 . 9

8 4 2 . 9 8 4 3 . O 8 4 3 . O 8 4 3 . O 8 4 3 . 1

8 4 3 . 1

8 4 1 . 4 8 4 1 . 5 8 4 1 . 5 8 4 1 . 5 8 4 1 . 6

8 4 1 . 6 8 4 1 . 7 8 4 1 . 7 8 4 1 . 7 8 4 1 . 8

8 4 1 . 8 8 4 1 . 8 8 4 1 . 9 8 4 1 . 9 8 4 1 . 9

8 4 2 . O 8 4 2 . O 8 4 2 . O 8 4 2 . 1 8 4 2 . 1

8 4 2 . 2 8 4 2 . 2 8 4 2 . 2 8 4 2 . 3 8 4 2 . 3

8 4 2 . 3 8 4 2 . 4 8 4 2 . 4 8 4 2 . 4 8 4 2 . 5

8 4 2 . 5 8 4 2 . 5 8 4 2 . 6 8 4 2 . 6 8 4 2 . 6

8 4 2 . 7 8 4 2 . 7 8 4 2 . 8 8 4 2 . 8 8 4 2 . 8

8 4 2 . 9 8 4 2 . 9 8 4 2 . 9 8 4 3 . O 8 4 3 . O

8 4 3 . O 8 4 3 . 1 8 4 3 . 1 8 4 3 . 1 8 4 3 . 2

8 4 3 . 2

8 4 1 . 5 8 4 1 . 6 8 4 1 . 6 8 4 1 . 6 8 4 1 . 7

8 4 1 . 7 8 4 1 . 8 8 4 1 . 8 8 4 1 . 8 8 4 1 . 9

8 4 1 . 9 8 4 1 . 9 8 4 2 . O 8 4 2 . O 8 4 2 . O

8 4 2 . 1 8 4 2 . 1 8 4 2 . 1 8 4 2 . 2 8 4 2 . 2

8 4 2 . 2 8 4 2 . 3 8 4 2 . 3 8 4 2 . 4 8 4 2 . 4

8 4 2 . 4 8 4 2 . 5 8 4 2 . 5 8 4 2 . 5 8 4 2 . 6

8 4 2 . 6 8 4 2 . 6 8 4 2 . 7 8 4 2 . 7 8 4 2 . 7

8 4 2 . 8 8 4 2 . 8 8 4 2 . 9 8 4 2 . 9 8 4 2 . 9

8 4 3 . O 8 4 3 . O 8 4 3 . O 8 4 3 . 1 8 4 3 . 1

8 4 3 . 1 8 4 3 . 2 8 4 3 . 2 8 4 3 . 2 8 4 3 . 3

8 4 3 . 3

8 4 1 . 6 8 4 1 . 7 8 4 1 . 7 8 4 1 . 7 8 4 1 . 8

8 4 1 . 8 8 4 1 . 9 8 4 1 . 9 8 4 1 . 9 8 4 2 . O

8 4 2 . O 8 4 2 . O 8 4 2 . 1 8 4 2 . 1 8 4 2 . 1

8 4 2 . 2 8 4 2 . 2 8 4 2 . 2 8 4 2 . 3 8 4 2 . 3

8 4 2 . 3 8 4 2 . 4 8 4 2 . 4 8 4 2 . 5 8 4 2 . 5

8 4 2 . 5 8 4 2 . 6 8 4 2 . 6 8 4 2 . 6 8 4 2 . 7

8 4 2 . 7 8 4 2 . 7 8 4 2 . 8 8 4 2 . 8 8 4 2 . 8

8 4 2 . 9 8 4 2 . 9 8 4 3 . O 8 4 3 . O 8 4 3 . O

8 4 3 . 1 8 4 3 . 1 8 4 3 . 1 8 4 3 . 2 8 4 3 . 2

8 4 3 . 2 8 4 3 . 3 8 4 3 . 3 8 4 3 . 3 8 4 3 . 4

8 4 3 . 4

8 4 1 . 7 8 4 1 . 8 8 4 1 . 8 8 4 1 . 8 8 4 1 . 9

8 4 1 . 9 8 4 2 . O 8 4 2 . O 8 4 2 . O 8 4 2 . 1

8 4 2 . 1 8 4 2 . 1 8 4 2 . 2 8 4 2 . 2 8 4 2 . 2

8 4 2 . 3 8 4 2 . 3 8 4 2 . 3 8 4 2 . 4 8 4 2 . 4

8 4 2 . 4 8 4 2 . 5 8 4 2 . 5 8 4 2 . 6 8 4 2 . 6

8 4 2 . 6 8 4 2 . 7 8 4 2 . 7 8 4 2 . 7 8 4 2 . 8

8 4 2 . 8 8 4 2 . 8 8 4 2 . 9 8 4 2 . 9 8 4 2 . 9

8 4 3 . O 8 4 3 . O 8 4 3 . 1 8 4 3 . 1 8 4 3 . 1

8 4 3 . 2 8 4 3 . 2 8 4 3 . 2 8 4 3 . 3 8 4 3 . 3

8 4 3 . 3 8 4 3 . 4 8 4 3 . 4 8 4 3 . 4 8 4 3 . 5

8 4 3 . 5

8 4 1 . 8 8 4 1 . 9 8 4 1 . 9 8 4 1 . 9 8 4 2 . O

8 4 2 . O 8 4 2 . 1 8 4 2 . 1 8 4 2 . 1 8 4 2 . 2

8 4 2 . 2 8 4 2 . 2 8 4 2 . 3 8 4 2 . 3 8 4 2 . 3

8 4 2 . 4 8 4 2 . 4 8 4 2 . 4 8 4 2 . 5 8 4 2 . 5

8 4 2 . 5 8 4 2 . 6 8 4 2 . 6 8 4 2 . 7 8 4 2 . 7

8 4 2 . 7 8 4 2 . 8 8 4 2 . 8 8 4 2 . 8 8 4 2 . 9

8 4 2 . 9 8 4 2 . 9 8 4 3 . O 8 4 3 . O 8 4 3 . O

8 4 3 . 1 8 4 3 . 1 8 4 3 . 2 8 4 3 . 2 8 4 3 . 2

8 4 3 . 3 8 4 3 . 3 8 4 3 . 3 8 4 3 . 4 8 4 3 . 4

8 4 3 . 4 8 4 3 . 5 8 4 3 . 5 8 4 3 . 5 8 4 3 . 6

8 4 3 . 6

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 3 5 . 1 5 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 3 5 . 3 5 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 3 5 . 5 5 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 3 5 . 8 5 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.13 Instructions to Generate Table 53D - Correction of Observed Density to Density at 15°C for Generalized Lubricating Oils


Output Variables: Base density at 15'C and O Wa (gauge).

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Hold pressure value at O Wa.



Determine the base density using procedure in 11.1.7.2 & specimng commodity group "D." Round the resulting density value for display consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 53D. Correction of Observed Density to 15'C Base Density (Lube Oils) If hydrometer used to determine density, apply glass correction before entering table

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 3 5 . 1 5 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 3 5 . 3 5 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 3 5 . 5 5 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 3 5 . 8 5 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0




8 3 9 . 6 8 3 9 . 6 8 3 9 . 7 8 3 9 . 7 8 3 9 . 7

8 3 9 . 8 8 3 9 . 8 8 3 9 . 8 8 3 9 . 9 8 3 9 . 9

8 3 9 . 9 8 4 0 . O 8 4 0 . O 8 4 0 . O 8 4 0 . 1

8 4 0 . 1 8 4 0 . 1 8 4 0 . 1 8 4 0 . 2 8 4 0 . 2

8 4 0 . 2 8 4 0 . 3 8 4 0 . 3 8 4 0 . 3 8 4 0 . 4

8 4 0 . 4 8 4 0 . 4 8 4 0 . 5 8 4 0 . 5 8 4 0 . 5

8 4 0 . 6 8 4 0 . 6 8 4 0 . 6 8 4 0 . 7 8 4 0 . 7

8 4 0 . 7 8 4 0 . 8 8 4 0 . 8 8 4 0 . 8 8 4 0 . 8

8 4 0 . 9 8 4 0 . 9 8 4 0 . 9 8 4 1 . 0 8 4 1 . 0

8 4 1 . 0 8 4 1 . 1 8 4 1 . 1 8 4 1 . 1 8 4 1 . 2

8 4 1 . 2

8 3 9 . 7 8 3 9 . 7 8 3 9 . 8 8 3 9 . 8 8 3 9 . 8

8 3 9 . 9 8 3 9 . 9 8 3 9 . 9 8 4 0 . O 8 4 0 . O

8 4 0 . O 8 4 0 . 1 8 4 0 . 1 8 4 0 . 1 8 4 0 . 2

8 4 0 . 2 8 4 0 . 2 8 4 0 . 2 8 4 0 . 3 8 4 0 . 3

8 4 0 . 3 8 4 0 . 4 8 4 0 . 4 8 4 0 . 4 8 4 0 . 5

8 4 0 . 5 8 4 0 . 5 8 4 0 . 6 8 4 0 . 6 8 4 0 . 6

8 4 0 . 7 8 4 0 . 7 8 4 0 . 7 8 4 0 . 8 8 4 0 . 8

8 4 0 . 8 8 4 0 . 9 8 4 0 . 9 8 4 0 . 9 8 4 0 . 9

8 4 1 . 0 8 4 1 . 0 8 4 1 . 0 8 4 1 . 1 8 4 1 . 1

8 4 1 . 1 8 4 1 . 2 8 4 1 . 2 8 4 1 . 2 8 4 1 . 3

8 4 1 . 3

8 3 9 . 8 8 3 9 . 8 8 3 9 . 9 8 3 9 . 9 8 3 9 . 9

8 4 0 . O 8 4 0 . O 8 4 0 . O 8 4 0 . 1 8 4 0 . 1

8 4 0 . 1 8 4 0 . 2 8 4 0 . 2 8 4 0 . 2 8 4 0 . 3

8 4 0 . 3 8 4 0 . 3 8 4 0 . 3 8 4 0 . 4 8 4 0 . 4

8 4 0 . 4 8 4 0 . 5 8 4 0 . 5 8 4 0 . 5 8 4 0 . 6

8 4 0 . 6 8 4 0 . 6 8 4 0 . 7 8 4 0 . 7 8 4 0 . 7

8 4 0 . 8 8 4 0 . 8 8 4 0 . 8 8 4 0 . 9 8 4 0 . 9

8 4 0 . 9 8 4 1 . 0 8 4 1 . 0 8 4 1 . 0 8 4 1 . 0

8 4 1 . 1 8 4 1 . 1 8 4 1 . 1 8 4 1 . 2 8 4 1 . 2

8 4 1 . 2 8 4 1 . 3 8 4 1 . 3 8 4 1 . 3 8 4 1 . 4

8 4 1 . 4

8 3 9 . 9 8 3 9 . 9 8 4 0 . O 8 4 0 . O 8 4 0 . O

8 4 0 . 1 8 4 0 . 1 8 4 0 . 1 8 4 0 . 2 8 4 0 . 2

8 4 0 . 2 8 4 0 . 3 8 4 0 . 3 8 4 0 . 3 8 4 0 . 4

8 4 0 . 4 8 4 0 . 4 8 4 0 . 4 8 4 0 . 5 8 4 0 . 5

8 4 0 . 5 8 4 0 . 6 8 4 0 . 6 8 4 0 . 6 8 4 0 . 7

8 4 0 . 7 8 4 0 . 7 8 4 0 . 8 8 4 0 . 8 8 4 0 . 8

8 4 0 . 9 8 4 0 . 9 8 4 0 . 9 8 4 1 . 0 8 4 1 . 0

8 4 1 . 0 8 4 1 . 1 8 4 1 . 1 8 4 1 . 1 8 4 1 . 1

8 4 1 . 2 8 4 1 . 2 8 4 1 . 2 8 4 1 . 3 8 4 1 . 3

8 4 1 . 3 8 4 1 . 4 8 4 1 . 4 8 4 1 . 4 8 4 1 . 5

8 4 1 . 5

8 4 0 . O 8 4 0 . O 8 4 0 . 1 8 4 0 . 1 8 4 0 . 1

8 4 0 . 2 8 4 0 . 2 8 4 0 . 2 8 4 0 . 3 8 4 0 . 3

8 4 0 . 3 8 4 0 . 4 8 4 0 . 4 8 4 0 . 4 8 4 0 . 5

8 4 0 . 5 8 4 0 . 5 8 4 0 . 5 8 4 0 . 6 8 4 0 . 6

8 4 0 . 6 8 4 0 . 7 8 4 0 . 7 8 4 0 . 7 8 4 0 . 8

8 4 0 . 8 8 4 0 . 8 8 4 0 . 9 8 4 0 . 9 8 4 0 . 9

8 4 1 . 0 8 4 1 . 0 8 4 1 . 0 8 4 1 . 1 8 4 1 . 1

8 4 1 . 1 8 4 1 . 2 8 4 1 . 2 8 4 1 . 2 8 4 1 . 2

8 4 1 . 3 8 4 1 . 3 8 4 1 . 3 8 4 1 . 4 8 4 1 . 4

8 4 1 . 4 8 4 1 . 5 8 4 1 . 5 8 4 1 . 5 8 4 1 . 6

8 4 1 . 6

8 4 0 . 1 8 4 0 . 1 8 4 0 . 2 8 4 0 . 2 8 4 0 . 2

8 4 0 . 3 8 4 0 . 3 8 4 0 . 3 8 4 0 . 4 8 4 0 . 4

8 4 0 . 4 8 4 0 . 5 8 4 0 . 5 8 4 0 . 5 8 4 0 . 6

8 4 0 . 6 8 4 0 . 6 8 4 0 . 6 8 4 0 . 7 8 4 0 . 7

8 4 0 . 7 8 4 0 . 8 8 4 0 . 8 8 4 0 . 8 8 4 0 . 9

8 4 0 . 9 8 4 0 . 9 8 4 1 . 0 8 4 1 . 0 8 4 1 . 0

8 4 1 . 1 8 4 1 . 1 8 4 1 . 1 8 4 1 . 2 8 4 1 . 2

8 4 1 . 2 8 4 1 . 3 8 4 1 . 3 8 4 1 . 3 8 4 1 . 3

8 4 1 . 4 8 4 1 . 4 8 4 1 . 4 8 4 1 . 5 8 4 1 . 5

8 4 1 . 5 8 4 1 . 6 8 4 1 . 6 8 4 1 . 6 8 4 1 . 7

8 4 1 . 7

8 4 0 . 2 8 4 0 . 2 8 4 0 . 3 8 4 0 . 3 8 4 0 . 3

8 4 0 . 4 8 4 0 . 4 8 4 0 . 4 8 4 0 . 5 8 4 0 . 5

8 4 0 . 5 8 4 0 . 6 8 4 0 . 6 8 4 0 . 6 8 4 0 . 7

8 4 0 . 7 8 4 0 . 7 8 4 0 . 7 8 4 0 . 8 8 4 0 . 8

8 4 0 . 8 8 4 0 . 9 8 4 0 . 9 8 4 0 . 9 8 4 1 . 0

8 4 1 . 0 8 4 1 . 0 8 4 1 . 1 8 4 1 . 1 8 4 1 . 1

8 4 1 . 2 8 4 1 . 2 8 4 1 . 2 8 4 1 . 3 8 4 1 . 3

8 4 1 . 3 8 4 1 . 4 8 4 1 . 4 8 4 1 . 4 8 4 1 . 4

8 4 1 . 5 8 4 1 . 5 8 4 1 . 5 8 4 1 . 6 8 4 1 . 6

8 4 1 . 6 8 4 1 . 7 8 4 1 . 7 8 4 1 . 7 8 4 1 . 8

8 4 1 . 8

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 3 5 . 1 5 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 3 5 . 3 5 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 3 5 . 5 5 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 3 5 . 8 5 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.14 Instructions to Generate Tables 54A - Correction of Volume to 15°C Against Density at 15°C for Generalized Crude Oils

Input Variables: Base density and temperature. Pressure set to O Wa (gauge).

Output Variables: CTL at input temperature and O Wa (gauge).

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Hold pressure value at O Wa (gauge).


Increment temperature by 0.05’C in range of -50.00’ to 150.00’C. Ensure that the temperature value remains rounded consistent with instructions in 11.1.5.4.

Determine the CTL using procedure in 1 1.1.7.1 & speciQing commodity group “A.” Round the value for display consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 54A. Volume Correction Factor Due to Temperature Against 15'C Base Density (Crude Oils)

Alternate Pressure is O kPa (gauge)

Base Density (kg/m3) OC 925 . O 9 2 5 . 1 925 .2 9 2 5 . 3 925 .4 9 2 5 . 5 9 2 5 . 6 OC

Volume Correction for the Effect of Temperature on Liquid (CTL) to 15'C

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0

0 . 9 8 1 9 6 O . 9 8 1 9 2 O . 9 8 1 8 9 O . 9 8 1 8 5 O . 9 8 1 8 1

O . 9 8 1 7 8 O . 9 8 1 7 4 O . 9 8 1 7 1 O . 9 8 1 6 7 O . 9 8 1 6 3

O . 9 8 1 6 0 O . 9 8 1 5 6 O . 9 8 1 5 2 0 . 9 8 1 4 9 O . 9 8 1 4 5

O . 9 8 1 4 2 O . 9 8 1 3 8 O . 9 8 1 3 4 O . 9 8 1 3 1 O . 9 8 1 2 7

O . 9 8 1 2 3 O . 9 8 1 2 0 0 . 9 8 1 1 6 O . 9 8 1 1 3 O . 9 8 1 0 9

O . 9 8 1 0 5 O . 9 8 1 0 2 O . 9 8 0 9 8 O . 9 8 0 9 4 O . 9 8 0 9 1

O . 9 8 0 8 7 O . 9 8 0 8 4 O . 9 8 0 8 0 O . 9 8 0 7 6 O . 9 8 0 7 3

O . 9 8 0 6 9 O . 9 8 0 6 5 O . 9 8 0 6 2 O . 9 8 0 5 8 O . 9 8 0 5 5

O . 9 8 0 5 1 O . 9 8 0 4 7 O . 9 8 0 4 4 O . 9 8 0 4 0 O . 9 8 0 3 6

O . 9 8 0 3 3 O . 9 8 0 2 9 O . 9 8 0 2 5 O . 9 8 0 2 2 O . 9 8 0 1 8

O . 9 8 0 1 5

0 . 9 8 1 9 6 O . 9 8 1 9 3 O . 9 8 1 8 9 O . 9 8 1 8 6 O . 9 8 1 8 2

O . 9 8 1 7 8 O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 7 O . 9 8 1 6 4

O . 9 8 1 6 0 O . 9 8 1 5 6 O . 9 8 1 5 3 0 . 9 8 1 4 9 0 . 9 8 1 4 6

O . 9 8 1 4 2 O . 9 8 1 3 8 O . 9 8 1 3 5 O . 9 8 1 3 1 O . 9 8 1 2 7

O . 9 8 1 2 4 O . 9 8 1 2 0 O . 9 8 1 1 7 O . 9 8 1 1 3 O . 9 8 1 0 9

O . 9 8 1 0 6 O . 9 8 1 0 2 O . 9 8 0 9 8 O . 9 8 0 9 5 O . 9 8 0 9 1

O . 9 8 0 8 8 O . 9 8 0 8 4 O . 9 8 0 8 0 O . 9 8 0 7 7 O . 9 8 0 7 3

O . 9 8 0 6 9 O . 9 8 0 6 6 O . 9 8 0 6 2 O . 9 8 0 5 9 O . 9 8 0 5 5

O . 9 8 0 5 1 O . 9 8 0 4 8 O . 9 8 0 4 4 O . 9 8 0 4 0 O . 9 8 0 3 7

O . 9 8 0 3 3 O . 9 8 0 3 0 O . 9 8 0 2 6 O . 9 8 0 2 2 O . 9 8 0 1 9

O . 9 8 0 1 5

O . 9 8 1 9 7 O . 9 8 1 9 3 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 2

0 . 9 8 1 7 9 O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 8 O . 9 8 1 6 4

O . 9 8 1 6 1 O . 9 8 1 5 7 O . 9 8 1 5 3 O . 9 8 1 5 0 0 . 9 8 1 4 6

O . 9 8 1 4 2 O . 9 8 1 3 9 O . 9 8 1 3 5 O . 9 8 1 3 2 O . 9 8 1 2 8

O . 9 8 1 2 4 O . 9 8 1 2 1 O . 9 8 1 1 7 O . 9 8 1 1 3 O . 9 8 1 1 0

O . 9 8 1 0 6 O . 9 8 1 0 3 O . 9 8 0 9 9 O . 9 8 0 9 5 O . 9 8 0 9 2

O . 9 8 0 8 8 O . 9 8 0 8 4 O . 9 8 0 8 1 O . 9 8 0 7 7 O . 9 8 0 7 4

O . 9 8 0 7 0 O . 9 8 0 6 6 O . 9 8 0 6 3 O . 9 8 0 5 9 O . 9 8 0 5 5

O . 9 8 0 5 2 O . 9 8 0 4 8 O . 9 8 0 4 4 O . 9 8 0 4 1 O . 9 8 0 3 7

O . 9 8 0 3 4 O . 9 8 0 3 0 O . 9 8 0 2 6 O . 9 8 0 2 3 O . 9 8 0 1 9

O . 9 8 0 1 5

O . 9 8 1 9 7 O . 9 8 1 9 4 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 3

0 . 9 8 1 7 9 O . 9 8 1 7 5 O . 9 8 1 7 2 O . 9 8 1 6 8 O . 9 8 1 6 5

O . 9 8 1 6 1 O . 9 8 1 5 7 O . 9 8 1 5 4 O . 9 8 1 5 0 0 . 9 8 1 4 6

O . 9 8 1 4 3 O . 9 8 1 3 9 O . 9 8 1 3 6 O . 9 8 1 3 2 O . 9 8 1 2 8

O . 9 8 1 2 5 O . 9 8 1 2 1 O . 9 8 1 1 7 O . 9 8 1 1 4 O . 9 8 1 1 0

O . 9 8 1 0 7 O . 9 8 1 0 3 O . 9 8 0 9 9 O . 9 8 0 9 6 O . 9 8 0 9 2

O . 9 8 0 8 8 O . 9 8 0 8 5 O . 9 8 0 8 1 O . 9 8 0 7 8 O . 9 8 0 7 4

O . 9 8 0 7 0 O . 9 8 0 6 7 O . 9 8 0 6 3 O . 9 8 0 5 9 O . 9 8 0 5 6

O . 9 8 0 5 2 O . 9 8 0 4 9 O . 9 8 0 4 5 O . 9 8 0 4 1 O . 9 8 0 3 8

O . 9 8 0 3 4 O . 9 8 0 3 0 O . 9 8 0 2 7 O . 9 8 0 2 3 O . 9 8 0 2 0

O . 9 8 0 1 6

O . 9 8 1 9 8 O . 9 8 1 9 4 O . 9 8 1 9 0 O . 9 8 1 8 7 O . 9 8 1 8 3

0 . 9 8 1 7 9 0 . 9 8 1 7 6 O . 9 8 1 7 2 O . 9 8 1 6 9 O . 9 8 1 6 5

O . 9 8 1 6 1 O . 9 8 1 5 8 O . 9 8 1 5 4 O . 9 8 1 5 0 O . 9 8 1 4 7

O . 9 8 1 4 3 O . 9 8 1 4 0 O . 9 8 1 3 6 O . 9 8 1 3 2 O . 9 8 1 2 9

O . 9 8 1 2 5 O . 9 8 1 2 1 O . 9 8 1 1 8 O . 9 8 1 1 4 O . 9 8 1 1 1

O . 9 8 1 0 7 O . 9 8 1 0 3 O . 9 8 1 0 0 O . 9 8 0 9 6 O . 9 8 0 9 2

O . 9 8 0 8 9 O . 9 8 0 8 5 O . 9 8 0 8 2 O . 9 8 0 7 8 O . 9 8 0 7 4

O . 9 8 0 7 1 O . 9 8 0 6 7 O . 9 8 0 6 3 O . 9 8 0 6 0 O . 9 8 0 5 6

O . 9 8 0 5 3 O . 9 8 0 4 9 O . 9 8 0 4 5 O . 9 8 0 4 2 O . 9 8 0 3 8

O . 9 8 0 3 4 O . 9 8 0 3 1 O . 9 8 0 2 7 O . 9 8 0 2 4 O . 9 8 0 2 0

O . 9 8 0 1 6

O . 9 8 1 9 8 O . 9 8 1 9 4 O . 9 8 1 9 1 O . 9 8 1 8 7 O . 9 8 1 8 3

O . 9 8 1 8 0 0 . 9 8 1 7 6 O . 9 8 1 7 3 O . 9 8 1 6 9 O . 9 8 1 6 5

0 . 9 8 1 6 2 O . 9 8 1 5 8 O . 9 8 1 5 4 O . 9 8 1 5 1 O . 9 8 1 4 7

O . 9 8 1 4 4 O . 9 8 1 4 0 O . 9 8 1 3 6 O . 9 8 1 3 3 O . 9 8 1 2 9

O . 9 8 1 2 5 O . 9 8 1 2 2 O . 9 8 1 1 8 O . 9 8 1 1 5 O . 9 8 1 1 1

O . 9 8 1 0 7 O . 9 8 1 0 4 O . 9 8 1 0 0 O . 9 8 0 9 7 O . 9 8 0 9 3

O . 9 8 0 8 9 O . 9 8 0 8 6 O . 9 8 0 8 2 O . 9 8 0 7 8 O . 9 8 0 7 5

O . 9 8 0 7 1 O . 9 8 0 6 8 O . 9 8 0 6 4 O . 9 8 0 6 0 O . 9 8 0 5 7

O . 9 8 0 5 3 O . 9 8 0 4 9 O . 9 8 0 4 6 O . 9 8 0 4 2 O . 9 8 0 3 9

O . 9 8 0 3 5 O . 9 8 0 3 1 O . 9 8 0 2 8 O . 9 8 0 2 4 O . 9 8 0 2 0

O . 9 8 0 1 7

O . 9 8 1 9 8 O . 9 8 1 9 5 O . 9 8 1 9 1 O . 9 8 1 8 7 O . 9 8 1 8 4

O . 9 8 1 8 0 O . 9 8 1 7 7 O . 9 8 1 7 3 O . 9 8 1 6 9 O . 9 8 1 6 6

0 . 9 8 1 6 2 O . 9 8 1 5 9 O . 9 8 1 5 5 O . 9 8 1 5 1 O . 9 8 1 4 8

O . 9 8 1 4 4 O . 9 8 1 4 0 O . 9 8 1 3 7 O . 9 8 1 3 3 O . 9 8 1 3 0

O . 9 8 1 2 6 O . 9 8 1 2 2 0 . 9 8 1 1 9 O . 9 8 1 1 5 O . 9 8 1 1 1

O . 9 8 1 0 8 O . 9 8 1 0 4 O . 9 8 1 0 1 O . 9 8 0 9 7 O . 9 8 0 9 3

O . 9 8 0 9 0 O . 9 8 0 8 6 O . 9 8 0 8 2 O . 9 8 0 7 9 O . 9 8 0 7 5

O . 9 8 0 7 2 O . 9 8 0 6 8 O . 9 8 0 6 4 O . 9 8 0 6 1 O . 9 8 0 5 7

O . 9 8 0 5 3 O . 9 8 0 5 0 O . 9 8 0 4 6 O . 9 8 0 4 3 O . 9 8 0 3 9

O . 9 8 0 3 5 O . 9 8 0 3 2 O . 9 8 0 2 8 O . 9 8 0 2 4 O . 9 8 0 2 1

O . 9 8 0 1 7

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.15 Instructions to Generate Tables 54B - Correction of Volume to 15°C Against Density at 15°C for Generalized Products



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:




Determine the CTL using procedure in 11.1.7.1 & specifjdng commodity group "B." Round the value for display consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 54B. Volume Correction Factor Due to Temperature Against 15'C Base Density (Refined Products)


OC

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0

Base Density (kg/m3) 925 . O 9 2 5 . 1 925 .2 9 2 5 . 3 925 .4

Volume Correction for the Effect of Temperature on

0 . 9 8 1 2 9 0 . 9 8 1 3 0 0 . 9 8 1 3 0 0 . 9 8 1 3 0 0 . 9 8 1 3 0 0 . 9 8 1 2 6 0 . 9 8 1 2 6 0 . 9 8 1 2 6 0 . 9 8 1 2 6 0 . 9 8 1 2 7 0 . 9 8 1 2 2 0 . 9 8 1 2 2 0 . 9 8 1 2 2 0 . 9 8 1 2 3 0 . 9 8 1 2 3 0 . 9 8 1 1 8 0 . 9 8 1 1 8 0 . 9 8 1 1 9 0 . 9 8 1 1 9 0 . 9 8 1 1 9 0 . 9 8 1 1 4 0 . 9 8 1 1 5 0 . 9 8 1 1 5 0 . 9 8 1 1 5 0 . 9 8 1 1 5

0 . 9 8 1 1 1 0 . 9 8 1 1 1 0 . 9 8 1 1 1 0 . 9 8 1 1 1 0 . 9 8 1 1 2 0 . 9 8 1 0 7 0 . 9 8 1 0 7 0 . 9 8 1 0 7 0 . 9 8 1 0 8 0 . 9 8 1 0 8 0 . 9 8 1 0 3 0 . 9 8 1 0 3 0 . 9 8 1 0 4 0 . 9 8 1 0 4 0 . 9 8 1 0 4 0 . 9 8 0 9 9 0 . 9 8 1 0 0 0 . 9 8 1 0 0 0 . 9 8 1 0 0 0 . 9 8 1 0 0 0 . 9 8 0 9 6 0 . 9 8 0 9 6 0 . 9 8 0 9 6 0 . 9 8 0 9 6 0 . 9 8 0 9 7

0 . 9 8 0 9 2 0 . 9 8 0 9 2 0 . 9 8 0 9 2 0 . 9 8 0 9 3 0 . 9 8 0 9 3 0 . 9 8 0 8 8 0 . 9 8 0 8 8 0 . 9 8 0 8 9 0 . 9 8 0 8 9 0 . 9 8 0 8 9 0 . 9 8 0 8 4 0 . 9 8 0 8 5 0 . 9 8 0 8 5 0 . 9 8 0 8 5 0 . 9 8 0 8 5 0 . 9 8 0 8 1 0 . 9 8 0 8 1 0 . 9 8 0 8 1 0 . 9 8 0 8 1 0 . 9 8 0 8 2 0 . 9 8 0 7 7 0 . 9 8 0 7 7 0 . 9 8 0 7 7 0 . 9 8 0 7 8 0 . 9 8 0 7 8

0 . 9 8 0 7 3 0 . 9 8 0 7 3 0 . 9 8 0 7 4 0 . 9 8 0 7 4 0 . 9 8 0 7 4 0 . 9 8 0 6 9 0 . 9 8 0 7 0 0 . 9 8 0 7 0 0 . 9 8 0 7 0 0 . 9 8 0 7 0 0 . 9 8 0 6 6 0 . 9 8 0 6 6 0 . 9 8 0 6 6 0 . 9 8 0 6 6 0 . 9 8 0 6 7 O . 9 8 0 6 2 O . 9 8 0 6 2 O . 9 8 0 6 2 O . 9 8 0 6 3 O . 9 8 0 6 3 0 . 9 8 0 5 8 0 . 9 8 0 5 8 0 . 9 8 0 5 9 0 . 9 8 0 5 9 0 . 9 8 0 5 9

0 . 9 8 0 5 4 0 . 9 8 0 5 4 0 . 9 8 0 5 5 0 . 9 8 0 5 5 0 . 9 8 0 5 5 0 . 9 8 0 5 0 0 . 9 8 0 5 1 0 . 9 8 0 5 1 0 . 9 8 0 5 1 0 . 9 8 0 5 2 0 . 9 8 0 4 7 0 . 9 8 0 4 7 0 . 9 8 0 4 7 0 . 9 8 0 4 8 0 . 9 8 0 4 8 0 . 9 8 0 4 3 0 . 9 8 0 4 3 0 . 9 8 0 4 3 0 . 9 8 0 4 4 0 . 9 8 0 4 4 0 . 9 8 0 3 9 0 . 9 8 0 3 9 0 . 9 8 0 4 0 0 . 9 8 0 4 0 0 . 9 8 0 4 0

0 . 9 8 0 3 5 0 . 9 8 0 3 6 0 . 9 8 0 3 6 0 . 9 8 0 3 6 0 . 9 8 0 3 7 0 . 9 8 0 3 2 0 . 9 8 0 3 2 0 . 9 8 0 3 2 0 . 9 8 0 3 2 0 . 9 8 0 3 3 0 . 9 8 0 2 8 0 . 9 8 0 2 8 0 . 9 8 0 2 8 0 . 9 8 0 2 9 0 . 9 8 0 2 9 0 . 9 8 0 2 4 0 . 9 8 0 2 4 0 . 9 8 0 2 5 0 . 9 8 0 2 5 0 . 9 8 0 2 5 0 . 9 8 0 2 0 0 . 9 8 0 2 1 0 . 9 8 0 2 1 0 . 9 8 0 2 1 0 . 9 8 0 2 1

0 . 9 8 0 1 7 0 . 9 8 0 1 7 0 . 9 8 0 1 7 0 . 9 8 0 1 7 0 . 9 8 0 1 8 0 . 9 8 0 1 3 0 . 9 8 0 1 3 0 . 9 8 0 1 3 0 . 9 8 0 1 4 0 . 9 8 0 1 4 0 . 9 8 0 0 9 0 . 9 8 0 0 9 0 . 9 8 0 1 0 0 . 9 8 0 1 0 0 . 9 8 0 1 0 0 . 9 8 0 0 5 0 . 9 8 0 0 6 0 . 9 8 0 0 6 0 . 9 8 0 0 6 0 . 9 8 0 0 6 0 . 9 8 0 0 2 0 . 9 8 0 0 2 0 . 9 8 0 0 2 0 . 9 8 0 0 2 0 . 9 8 0 0 3

0 . 9 7 9 9 8 0 . 9 7 9 9 8 0 . 9 7 9 9 8 0 . 9 7 9 9 9 0 . 9 7 9 9 9 0 . 9 7 9 9 4 0 . 9 7 9 9 4 0 . 9 7 9 9 5 0 . 9 7 9 9 5 0 . 9 7 9 9 5 0 . 9 7 9 9 0 0 . 9 7 9 9 1 0 . 9 7 9 9 1 0 . 9 7 9 9 1 0 . 9 7 9 9 1 0 . 9 7 9 8 6 0 . 9 7 9 8 7 0 . 9 7 9 8 7 0 . 9 7 9 8 7 0 . 9 7 9 8 8 0 . 9 7 9 8 3 0 . 9 7 9 8 3 0 . 9 7 9 8 3 0 . 9 7 9 8 4 0 . 9 7 9 8 4

0 . 9 7 9 7 9 0 . 9 7 9 7 9 0 . 9 7 9 8 0 0 . 9 7 9 8 0 0 . 9 7 9 8 0 0 . 9 7 9 7 5 0 . 9 7 9 7 5 0 . 9 7 9 7 6 0 . 9 7 9 7 6 0 . 9 7 9 7 6 0 . 9 7 9 7 1 0 . 9 7 9 7 2 0 . 9 7 9 7 2 0 . 9 7 9 7 2 0 . 9 7 9 7 3 0 . 9 7 9 6 8 0 . 9 7 9 6 8 0 . 9 7 9 6 8 0 . 9 7 9 6 9 0 . 9 7 9 6 9 0 . 9 7 9 6 4 0 . 9 7 9 6 4 0 . 9 7 9 6 4 0 . 9 7 9 6 5 0 . 9 7 9 6 5

0 . 9 7 9 6 0 0 . 9 7 9 6 0 0 . 9 7 9 6 1 0 . 9 7 9 6 1 0 . 9 7 9 6 1 0 . 9 7 9 5 6 0 . 9 7 9 5 7 0 . 9 7 9 5 7 0 . 9 7 9 5 7 0 . 9 7 9 5 8 0 . 9 7 9 5 3 0 . 9 7 9 5 3 0 . 9 7 9 5 3 0 . 9 7 9 5 3 0 . 9 7 9 5 4 0 . 9 7 9 4 9 0 . 9 7 9 4 9 0 . 9 7 9 4 9 0 . 9 7 9 5 0 0 . 9 7 9 5 0 0 . 9 7 9 4 5 0 . 9 7 9 4 5 0 . 9 7 9 4 6 0 . 9 7 9 4 6 0 . 9 7 9 4 6

0 . 9 7 9 4 1 0 . 9 7 9 4 2 0 . 9 7 9 4 2 0 . 9 7 9 4 2 0 . 9 7 9 4 2

9 2 5 . 5 9 2 5 . 6 OC

Liquid (CTL) to 15'C

O . 9 8 1 3 1 O . 9 8 1 3 1 O . 9 8 1 2 7 O . 9 8 1 2 7 O . 9 8 1 2 3 O . 9 8 1 2 4 0 . 9 8 1 1 9 0 . 9 8 1 2 0 0 . 9 8 1 1 6 0 . 9 8 1 1 6

O . 9 8 1 1 2 O . 9 8 1 1 2 O . 9 8 1 0 8 O . 9 8 1 0 8 O . 9 8 1 0 4 O . 9 8 1 0 5 O . 9 8 1 0 1 O . 9 8 1 0 1 O . 9 8 0 9 7 O . 9 8 0 9 7

O . 9 8 0 9 3 O . 9 8 0 9 3 O . 9 8 0 8 9 O . 9 8 0 9 0 O . 9 8 0 8 6 O . 9 8 0 8 6 O . 9 8 0 8 2 O . 9 8 0 8 2 O . 9 8 0 7 8 O . 9 8 0 7 8

O . 9 8 0 7 4 O . 9 8 0 7 5 O . 9 8 0 7 1 O . 9 8 0 7 1 O . 9 8 0 6 7 O . 9 8 0 6 7 O . 9 8 0 6 3 O . 9 8 0 6 3 O . 9 8 0 5 9 O . 9 8 0 6 0

O . 9 8 0 5 6 O . 9 8 0 5 6 O . 9 8 0 5 2 O . 9 8 0 5 2 O . 9 8 0 4 8 O . 9 8 0 4 8 O . 9 8 0 4 4 O . 9 8 0 4 5 O . 9 8 0 4 1 O . 9 8 0 4 1

O . 9 8 0 3 7 O . 9 8 0 3 7 O . 9 8 0 3 3 O . 9 8 0 3 3 O . 9 8 0 2 9 O . 9 8 0 3 0 0 . 9 8 0 2 6 0 . 9 8 0 2 6 O . 9 8 0 2 2 O . 9 8 0 2 2

O . 9 8 0 1 8 O . 9 8 0 1 8 O . 9 8 0 1 4 O . 9 8 0 1 5 O . 9 8 0 1 0 O . 9 8 0 1 1 O . 9 8 0 0 7 O . 9 8 0 0 7 O . 9 8 0 0 3 O . 9 8 0 0 3

0 . 9 7 9 9 9 0 . 9 7 9 9 9 0 . 9 7 9 9 5 0 . 9 7 9 9 6 0 . 9 7 9 9 2 0 . 9 7 9 9 2 O . 9 7 9 8 8 O . 9 7 9 8 8 O . 9 7 9 8 4 O . 9 7 9 8 4

O . 9 7 9 8 0 O . 9 7 9 8 1 0 . 9 7 9 7 7 0 . 9 7 9 7 7 0 . 9 7 9 7 3 0 . 9 7 9 7 3 0 . 9 7 9 6 9 0 . 9 7 9 6 9 0 . 9 7 9 6 5 0 . 9 7 9 6 6

0 . 9 7 9 6 2 0 . 9 7 9 6 2 O . 9 7 9 5 8 O . 9 7 9 5 8 O . 9 7 9 5 4 O . 9 7 9 5 4 O . 9 7 9 5 0 O . 9 7 9 5 1 0 . 9 7 9 4 7 0 . 9 7 9 4 7

0 . 9 7 9 4 3 0 . 9 7 9 4 3

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.16 Instructions to Generate Tables 54D - Correction of Volume to 15°C Against Density at 15°C for Generalized Lubricating Oils



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:




Determine the CTL using procedure in 1 1.1.7.1 & speciQing commodity group "D." Round the value for display consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 54D. Volume Correction Factor Due to Temperature Against 15'C Base Density (Lube Oils)




4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0

O . 9 8 2 9 5 O . 9 8 2 9 1 O . 9 8 2 8 8 O . 9 8 2 8 5 O . 9 8 2 8 1

O . 9 8 2 7 8 O . 9 8 2 7 4 O . 9 8 2 7 1 O . 9 8 2 6 7 O . 9 8 2 6 4

O . 9 8 2 6 1 O . 9 8 2 5 7 O . 9 8 2 5 4 O . 9 8 2 5 0 O . 9 8 2 4 7

O . 9 8 2 4 3 O . 9 8 2 4 0 O . 9 8 2 3 7 O . 9 8 2 3 3 O . 9 8 2 3 0

O . 9 8 2 2 6 O . 9 8 2 2 3 0 . 9 8 2 1 9 0 . 9 8 2 1 6 O . 9 8 2 1 3

O . 9 8 2 0 9 O . 9 8 2 0 6 O . 9 8 2 0 2 0 . 9 8 1 9 9 O . 9 8 1 9 5

O . 9 8 1 9 2 O . 9 8 1 8 9 O . 9 8 1 8 5 O . 9 8 1 8 2 O . 9 8 1 7 8

O . 9 8 1 7 5 O . 9 8 1 7 1 O . 9 8 1 6 8 O . 9 8 1 6 5 O . 9 8 1 6 1

O . 9 8 1 5 8 O . 9 8 1 5 4 O . 9 8 1 5 1 O . 9 8 1 4 7 O . 9 8 1 4 4

O . 9 8 1 4 1 O . 9 8 1 3 7 O . 9 8 1 3 4 O . 9 8 1 3 0 O . 9 8 1 2 7

O . 9 8 1 2 3

O . 9 8 2 9 5 O . 9 8 2 9 2 O . 9 8 2 8 8 O . 9 8 2 8 5 O . 9 8 2 8 1

O . 9 8 2 7 8 O . 9 8 2 7 4 O . 9 8 2 7 1 O . 9 8 2 6 8 O . 9 8 2 6 4

O . 9 8 2 6 1 O . 9 8 2 5 7 O . 9 8 2 5 4 O . 9 8 2 5 0 O . 9 8 2 4 7

O . 9 8 2 4 4 O . 9 8 2 4 0 O . 9 8 2 3 7 O . 9 8 2 3 3 O . 9 8 2 3 0

O . 9 8 2 2 6 O . 9 8 2 2 3 O . 9 8 2 2 0 0 . 9 8 2 1 6 O . 9 8 2 1 3

O . 9 8 2 0 9 O . 9 8 2 0 6 O . 9 8 2 0 2 0 . 9 8 1 9 9 0 . 9 8 1 9 6

O . 9 8 1 9 2 O . 9 8 1 8 9 O . 9 8 1 8 5 O . 9 8 1 8 2 O . 9 8 1 7 8

O . 9 8 1 7 5 O . 9 8 1 7 2 O . 9 8 1 6 8 O . 9 8 1 6 5 O . 9 8 1 6 1

O . 9 8 1 5 8 O . 9 8 1 5 4 O . 9 8 1 5 1 O . 9 8 1 4 8 O . 9 8 1 4 4

O . 9 8 1 4 1 O . 9 8 1 3 7 O . 9 8 1 3 4 O . 9 8 1 3 0 O . 9 8 1 2 7

O . 9 8 1 2 4

O . 9 8 2 9 5 O . 9 8 2 9 2 O . 9 8 2 8 8 O . 9 8 2 8 5 O . 9 8 2 8 1

O . 9 8 2 7 8 O . 9 8 2 7 5 O . 9 8 2 7 1 O . 9 8 2 6 8 O . 9 8 2 6 4

O . 9 8 2 6 1 O . 9 8 2 5 7 O . 9 8 2 5 4 O . 9 8 2 5 1 O . 9 8 2 4 7

O . 9 8 2 4 4 O . 9 8 2 4 0 O . 9 8 2 3 7 O . 9 8 2 3 4 O . 9 8 2 3 0

O . 9 8 2 2 7 O . 9 8 2 2 3 O . 9 8 2 2 0 0 . 9 8 2 1 6 O . 9 8 2 1 3

O . 9 8 2 1 0 O . 9 8 2 0 6 O . 9 8 2 0 3 0 . 9 8 1 9 9 0 . 9 8 1 9 6

O . 9 8 1 9 2 O . 9 8 1 8 9 O . 9 8 1 8 6 O . 9 8 1 8 2 0 . 9 8 1 7 9

O . 9 8 1 7 5 O . 9 8 1 7 2 O . 9 8 1 6 8 O . 9 8 1 6 5 0 . 9 8 1 6 2

O . 9 8 1 5 8 O . 9 8 1 5 5 O . 9 8 1 5 1 O . 9 8 1 4 8 O . 9 8 1 4 4

O . 9 8 1 4 1 O . 9 8 1 3 8 O . 9 8 1 3 4 O . 9 8 1 3 1 O . 9 8 1 2 7

O . 9 8 1 2 4

O . 9 8 2 9 5 O . 9 8 2 9 2 O . 9 8 2 8 9 O . 9 8 2 8 5 O . 9 8 2 8 2

O . 9 8 2 7 8 O . 9 8 2 7 5 O . 9 8 2 7 1 O . 9 8 2 6 8 O . 9 8 2 6 5

O . 9 8 2 6 1 O . 9 8 2 5 8 O . 9 8 2 5 4 O . 9 8 2 5 1 O . 9 8 2 4 7

O . 9 8 2 4 4 O . 9 8 2 4 1 O . 9 8 2 3 7 O . 9 8 2 3 4 O . 9 8 2 3 0

O . 9 8 2 2 7 O . 9 8 2 2 3 O . 9 8 2 2 0 O . 9 8 2 1 7 O . 9 8 2 1 3

O . 9 8 2 1 0 O . 9 8 2 0 6 O . 9 8 2 0 3 0 . 9 8 1 9 9 0 . 9 8 1 9 6

O . 9 8 1 9 3 O . 9 8 1 8 9 O . 9 8 1 8 6 O . 9 8 1 8 2 0 . 9 8 1 7 9

O . 9 8 1 7 5 O . 9 8 1 7 2 O . 9 8 1 6 9 O . 9 8 1 6 5 0 . 9 8 1 6 2

O . 9 8 1 5 8 O . 9 8 1 5 5 O . 9 8 1 5 1 O . 9 8 1 4 8 O . 9 8 1 4 5

O . 9 8 1 4 1 O . 9 8 1 3 8 O . 9 8 1 3 4 O . 9 8 1 3 1 O . 9 8 1 2 7

O . 9 8 1 2 4

0 . 9 8 2 9 6 O . 9 8 2 9 2 O . 9 8 2 8 9 O . 9 8 2 8 5 O . 9 8 2 8 2

O . 9 8 2 7 8 O . 9 8 2 7 5 O . 9 8 2 7 2 O . 9 8 2 6 8 O . 9 8 2 6 5

O . 9 8 2 6 1 O . 9 8 2 5 8 O . 9 8 2 5 4 O . 9 8 2 5 1 O . 9 8 2 4 8

O . 9 8 2 4 4 O . 9 8 2 4 1 O . 9 8 2 3 7 O . 9 8 2 3 4 O . 9 8 2 3 0

O . 9 8 2 2 7 O . 9 8 2 2 4 O . 9 8 2 2 0 O . 9 8 2 1 7 O . 9 8 2 1 3

O . 9 8 2 1 0 O . 9 8 2 0 6 O . 9 8 2 0 3 O . 9 8 2 0 0 0 . 9 8 1 9 6

O . 9 8 1 9 3 O . 9 8 1 8 9 O . 9 8 1 8 6 O . 9 8 1 8 2 0 . 9 8 1 7 9

0 . 9 8 1 7 6 O . 9 8 1 7 2 O . 9 8 1 6 9 O . 9 8 1 6 5 0 . 9 8 1 6 2

O . 9 8 1 5 9 O . 9 8 1 5 5 O . 9 8 1 5 2 O . 9 8 1 4 8 O . 9 8 1 4 5

O . 9 8 1 4 1 O . 9 8 1 3 8 O . 9 8 1 3 5 O . 9 8 1 3 1 O . 9 8 1 2 8

O . 9 8 1 2 4

0 . 9 8 2 9 6 O . 9 8 2 9 2 O . 9 8 2 8 9 O . 9 8 2 8 5 O . 9 8 2 8 2

0 . 9 8 2 7 9 O . 9 8 2 7 5 O . 9 8 2 7 2 O . 9 8 2 6 8 O . 9 8 2 6 5

O . 9 8 2 6 1 O . 9 8 2 5 8 O . 9 8 2 5 5 O . 9 8 2 5 1 O . 9 8 2 4 8

O . 9 8 2 4 4 O . 9 8 2 4 1 O . 9 8 2 3 8 O . 9 8 2 3 4 O . 9 8 2 3 1

O . 9 8 2 2 7 O . 9 8 2 2 4 O . 9 8 2 2 0 O . 9 8 2 1 7 O . 9 8 2 1 4

O . 9 8 2 1 0 O . 9 8 2 0 7 O . 9 8 2 0 3 O . 9 8 2 0 0 0 . 9 8 1 9 6

O . 9 8 1 9 3 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 3 0 . 9 8 1 7 9

0 . 9 8 1 7 6 O . 9 8 1 7 2 O . 9 8 1 6 9 O . 9 8 1 6 6 0 . 9 8 1 6 2

O . 9 8 1 5 9 O . 9 8 1 5 5 O . 9 8 1 5 2 O . 9 8 1 4 8 O . 9 8 1 4 5

O . 9 8 1 4 2 O . 9 8 1 3 8 O . 9 8 1 3 5 O . 9 8 1 3 1 O . 9 8 1 2 8

O . 9 8 1 2 4

0 . 9 8 2 9 6 O . 9 8 2 9 3 O . 9 8 2 8 9 O . 9 8 2 8 6 O . 9 8 2 8 2

0 . 9 8 2 7 9 O . 9 8 2 7 5 O . 9 8 2 7 2 O . 9 8 2 6 9 O . 9 8 2 6 5

0 . 9 8 2 6 2 O . 9 8 2 5 8 O . 9 8 2 5 5 O . 9 8 2 5 1 O . 9 8 2 4 8

O . 9 8 2 4 5 O . 9 8 2 4 1 O . 9 8 2 3 8 O . 9 8 2 3 4 O . 9 8 2 3 1

O . 9 8 2 2 7 O . 9 8 2 2 4 O . 9 8 2 2 1 O . 9 8 2 1 7 O . 9 8 2 1 4

O . 9 8 2 1 0 O . 9 8 2 0 7 O . 9 8 2 0 3 O . 9 8 2 0 0 O . 9 8 1 9 7

O . 9 8 1 9 3 O . 9 8 1 9 0 O . 9 8 1 8 6 O . 9 8 1 8 3 0 . 9 8 1 7 9

0 . 9 8 1 7 6 O . 9 8 1 7 3 O . 9 8 1 6 9 O . 9 8 1 6 6 0 . 9 8 1 6 2

O . 9 8 1 5 9 O . 9 8 1 5 5 O . 9 8 1 5 2 0 . 9 8 1 4 9 O . 9 8 1 4 5

O . 9 8 1 4 2 O . 9 8 1 3 8 O . 9 8 1 3 5 O . 9 8 1 3 1 O . 9 8 1 2 8

O . 9 8 1 2 5

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.17 Instructions to Generate Tables 59A - Correction of Observed Density to Density at 20°C for Generalized Crude Oils



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:




Determine the CTL using procedure in 1 1.1.7.2 & speciQing commodity group “A.” Round the value for display consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 59A. Correction of Observed Density to 20'C Base Density (Crude Oils) If hydrometer used to determine density, apply glass correction before entering table

OC

35 .00 3 5 . 0 5 35 .10 3 5 . 1 5 35 .20

3 5 . 2 5 35 .30 3 5 . 3 5 35 .40 3 5 . 4 5

35 .50 3 5 . 5 5 35 .60 3 5 . 6 5 35 .70

3 5 . 7 5 35 .80 3 5 . 8 5 35 .90 3 5 . 9 5

36 .00 3 6 . 0 5 36 .10 3 6 . 1 5 36 .20

3 6 . 2 5 36 .30 3 6 . 3 5 36 .40 3 6 . 4 5

36 .50 3 6 . 5 5 36 .60 3 6 . 6 5 36 .70

3 6 . 7 5 36 .80 3 6 . 8 5 36 .90 3 6 . 9 5

37 .00 3 7 . 0 5 37 .10 3 7 . 1 5 37 .20

3 7 . 2 5 37 .30 3 7 . 3 5 37 .40 3 7 . 4 5

37 .50


Observed Density (kg/m3) 827 .0 8 2 7 . 1 827 .2 8 2 7 . 3 827 .4 8 2 7 . 5 8 2 7 . 6


838 . O 8 3 8 . 1 8 3 8 . 1 8 3 8 . 1 838 .2

838 .2 838 .2 8 3 8 . 3 8 3 8 . 3 8 3 8 . 3

838 .4 838 .4 8 3 8 . 5 8 3 8 . 5 8 3 8 . 5

8 3 8 . 6 8 3 8 . 6 8 3 8 . 6 838 .7 838 .7

838 .7 8 3 8 . 8 8 3 8 . 8 8 3 8 . 9 8 3 8 . 9

8 3 8 . 9 839 . O 839 . O 839 . O 8 3 9 . 1

8 3 9 . 1 8 3 9 . 1 839 .2 839 .2 8 3 9 . 3

8 3 9 . 3 8 3 9 . 3 839 .4 839 .4 839 .4

8 3 9 . 5 8 3 9 . 5 8 3 9 . 5 8 3 9 . 6 8 3 9 . 6

839 .7 839 .7 839 .7 8 3 9 . 8 8 3 9 . 8

8 3 9 . 8

8 3 8 . 1 838 .2 838 .2 838 .2 8 3 8 . 3

8 3 8 . 3 8 3 8 . 3 838 .4 838 .4 838 .4

8 3 8 . 5 8 3 8 . 5 8 3 8 . 6 8 3 8 . 6 8 3 8 . 6

838 .7 838 .7 838 .7 8 3 8 . 8 8 3 8 . 8

8 3 8 . 8 8 3 8 . 9 8 3 8 . 9 839 . O 839 . O

839 . O 8 3 9 . 1 8 3 9 . 1 8 3 9 . 1 839 .2

839 .2 839 .2 8 3 9 . 3 8 3 9 . 3 8 3 9 . 3

839 .4 839 .4 8 3 9 . 5 8 3 9 . 5 8 3 9 . 5

8 3 9 . 6 8 3 9 . 6 8 3 9 . 6 839 .7 839 .7

839 .7 8 3 9 . 8 8 3 9 . 8 8 3 9 . 9 8 3 9 . 9

8 3 9 . 9

838 .2 838 .2 8 3 8 . 3 8 3 8 . 3 838 .4

838 .4 838 .4 8 3 8 . 5 8 3 8 . 5 8 3 8 . 5

8 3 8 . 6 8 3 8 . 6 8 3 8 . 6 838 .7 838 .7

8 3 8 . 8 8 3 8 . 8 8 3 8 . 8 8 3 8 . 9 8 3 8 . 9

8 3 8 . 9 839 . O 839 . O 839 . O 8 3 9 . 1

8 3 9 . 1 839 .2 839 .2 839 .2 8 3 9 . 3

8 3 9 . 3 8 3 9 . 3 839 .4 839 .4 839 .4

8 3 9 . 5 8 3 9 . 5 8 3 9 . 6 8 3 9 . 6 8 3 9 . 6

839 .7 839 .7 839 .7 8 3 9 . 8 8 3 9 . 8

8 3 9 . 8 8 3 9 . 9 8 3 9 . 9 840 . O 840 . O

840 . O

8 3 8 . 3 8 3 8 . 3 838 .4 838 .4 8 3 8 . 5

8 3 8 . 5 8 3 8 . 5 8 3 8 . 6 8 3 8 . 6 8 3 8 . 6

838 .7 838 .7 838 .7 8 3 8 . 8 8 3 8 . 8

8 3 8 . 9 8 3 8 . 9 8 3 8 . 9 839 . O 839 . O

839 . O 8 3 9 . 1 8 3 9 . 1 8 3 9 . 1 839 .2

839 .2 8 3 9 . 3 8 3 9 . 3 8 3 9 . 3 839 .4

839 .4 839 .4 8 3 9 . 5 8 3 9 . 5 8 3 9 . 5

8 3 9 . 6 8 3 9 . 6 839 .7 839 .7 839 .7

8 3 9 . 8 8 3 9 . 8 8 3 9 . 8 8 3 9 . 9 8 3 9 . 9

8 3 9 . 9 840 . O 840 . O 8 4 0 . 1 8 4 0 . 1

8 4 0 . 1

838 .4 838 .4 8 3 8 . 5 8 3 8 . 5 8 3 8 . 6

8 3 8 . 6 8 3 8 . 6 838 .7 838 .7 838 .7

8 3 8 . 8 8 3 8 . 8 8 3 8 . 8 8 3 8 . 9 8 3 8 . 9

839 . O 839 . O 839 . O 8 3 9 . 1 8 3 9 . 1

8 3 9 . 1 839 .2 839 .2 839 .2 8 3 9 . 3

8 3 9 . 3 839 .4 839 .4 839 .4 8 3 9 . 5

8 3 9 . 5 8 3 9 . 5 8 3 9 . 6 8 3 9 . 6 8 3 9 . 6

839 .7 839 .7 8 3 9 . 8 8 3 9 . 8 8 3 9 . 8

8 3 9 . 9 8 3 9 . 9 8 3 9 . 9 840 . O 840 . O

840 . O 8 4 0 . 1 8 4 0 . 1 840 .2 840 .2

840 .2

8 3 8 . 5 8 3 8 . 5 8 3 8 . 6 8 3 8 . 6 838 .7

838 .7 838 .7 8 3 8 . 8 8 3 8 . 8 8 3 8 . 8

8 3 8 . 9 8 3 8 . 9 8 3 8 . 9 839 . O 839 . O

8 3 9 . 1 8 3 9 . 1 8 3 9 . 1 839 .2 839 .2

839 .2 8 3 9 . 3 8 3 9 . 3 8 3 9 . 3 839 .4

839 .4 8 3 9 . 5 8 3 9 . 5 8 3 9 . 5 8 3 9 . 6

8 3 9 . 6 8 3 9 . 6 839 .7 839 .7 839 .7

8 3 9 . 8 8 3 9 . 8 8 3 9 . 9 8 3 9 . 9 8 3 9 . 9

840 . O 840 . O 840 . O 8 4 0 . 1 8 4 0 . 1

8 4 0 . 1 840 .2 840 .2 8 4 0 . 3 8 4 0 . 3

8 4 0 . 3

8 3 8 . 6 8 3 8 . 6 838 .7 838 .7 8 3 8 . 8

8 3 8 . 8 8 3 8 . 8 8 3 8 . 9 8 3 8 . 9 8 3 8 . 9

839 . O 839 . O 839 . O 8 3 9 . 1 8 3 9 . 1

839 .2 839 .2 839 .2 8 3 9 . 3 8 3 9 . 3

8 3 9 . 3 839 .4 839 .4 839 .4 8 3 9 . 5

8 3 9 . 5 8 3 9 . 6 8 3 9 . 6 8 3 9 . 6 839 .7

839 .7 839 .7 8 3 9 . 8 8 3 9 . 8 8 3 9 . 8

8 3 9 . 9 8 3 9 . 9 840 . O 840 . O 840 . O

8 4 0 . 1 8 4 0 . 1 8 4 0 . 1 840 .2 840 .2

840 .2 8 4 0 . 3 8 4 0 . 3 8 4 0 . 3 840 .4

840 .4

OC

35 .00 3 5 . 0 5 35 .10 3 5 . 1 5 35 .20

3 5 . 2 5 35 .30 3 5 . 3 5 35 .40 3 5 . 4 5

35 .50 3 5 . 5 5 35 .60 3 5 . 6 5 35 .70

3 5 . 7 5 35 .80 3 5 . 8 5 35 .90 3 5 . 9 5

36 .00 3 6 . 0 5 36 .10 3 6 . 1 5 36 .20

3 6 . 2 5 36 .30 3 6 . 3 5 36 .40 3 6 . 4 5

36 .50 3 6 . 5 5 36 .60 3 6 . 6 5 36 .70

3 6 . 7 5 36 .80 3 6 . 8 5 36 .90 3 6 . 9 5

37 .00 3 7 . 0 5 37 .10 3 7 . 1 5 37 .20

3 7 . 2 5 37 .30 3 7 . 3 5 37 .40 3 7 . 4 5

37 .50



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.18 Instructions to Generate Tables 59B - Correction of Observed Density to Density at 20°C for Generalized Products



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:








--`,,`,,,-`-`,,`,,`,`,,`---


Table 59B. Correction of Observed Density to 20'C Base Density (Refined Products) If hydrometer used to determine density, apply glass correction before entering table

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 3 5 . 1 5 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 3 5 . 3 5 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 3 5 . 5 5 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 3 5 . 8 5 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0




8 3 7 . 7 8 3 7 . 7 8 3 7 . 8 8 3 7 . 8 8 3 7 . 8

8 3 7 . 9 8 3 7 . 9 8 3 7 . 9 8 3 8 . O 8 3 8 . O

8 3 8 . O 8 3 8 . 1 8 3 8 . 1 8 3 8 . 2 8 3 8 . 2

8 3 8 . 2 8 3 8 . 3 8 3 8 . 3 8 3 8 . 3 8 3 8 . 4

8 3 8 . 4 8 3 8 . 4 8 3 8 . 5 8 3 8 . 5 8 3 8 . 5

8 3 8 . 6 8 3 8 . 6 8 3 8 . 7 8 3 8 . 7 8 3 8 . 7

8 3 8 . 8 8 3 8 . 8 8 3 8 . 8 8 3 8 . 9 8 3 8 . 9

8 3 8 . 9 8 3 9 . O 8 3 9 . O 8 3 9 . O 8 3 9 . 1

8 3 9 . 1 8 3 9 . 2 8 3 9 . 2 8 3 9 . 2 8 3 9 . 3

8 3 9 . 3 8 3 9 . 3 8 3 9 . 4 8 3 9 . 4 8 3 9 . 4

8 3 9 . 5

8 3 7 . 8 8 3 7 . 8 8 3 7 . 9 8 3 7 . 9 8 3 7 . 9

8 3 8 . O 8 3 8 . O 8 3 8 . O 8 3 8 . 1 8 3 8 . 1

8 3 8 . 1 8 3 8 . 2 8 3 8 . 2 8 3 8 . 3 8 3 8 . 3

8 3 8 . 3 8 3 8 . 4 8 3 8 . 4 8 3 8 . 4 8 3 8 . 5

8 3 8 . 5 8 3 8 . 5 8 3 8 . 6 8 3 8 . 6 8 3 8 . 6

8 3 8 . 7 8 3 8 . 7 8 3 8 . 8 8 3 8 . 8 8 3 8 . 8

8 3 8 . 9 8 3 8 . 9 8 3 8 . 9 8 3 9 . O 8 3 9 . O

8 3 9 . O 8 3 9 . 1 8 3 9 . 1 8 3 9 . 1 8 3 9 . 2

8 3 9 . 2 8 3 9 . 3 8 3 9 . 3 8 3 9 . 3 8 3 9 . 4

8 3 9 . 4 8 3 9 . 4 8 3 9 . 5 8 3 9 . 5 8 3 9 . 5

8 3 9 . 6

8 3 7 . 9 8 3 7 . 9 8 3 8 . O 8 3 8 . O 8 3 8 . O

8 3 8 . 1 8 3 8 . 1 8 3 8 . 1 8 3 8 . 2 8 3 8 . 2

8 3 8 . 2 8 3 8 . 3 8 3 8 . 3 8 3 8 . 4 8 3 8 . 4

8 3 8 . 4 8 3 8 . 5 8 3 8 . 5 8 3 8 . 5 8 3 8 . 6

8 3 8 . 6 8 3 8 . 6 8 3 8 . 7 8 3 8 . 7 8 3 8 . 7

8 3 8 . 8 8 3 8 . 8 8 3 8 . 9 8 3 8 . 9 8 3 8 . 9

8 3 9 . O 8 3 9 . O 8 3 9 . O 8 3 9 . 1 8 3 9 . 1

8 3 9 . 1 8 3 9 . 2 8 3 9 . 2 8 3 9 . 2 8 3 9 . 3

8 3 9 . 3 8 3 9 . 4 8 3 9 . 4 8 3 9 . 4 8 3 9 . 5

8 3 9 . 5 8 3 9 . 5 8 3 9 . 6 8 3 9 . 6 8 3 9 . 6

8 3 9 . 7

8 3 8 . O 8 3 8 . O 8 3 8 . 1 8 3 8 . 1 8 3 8 . 1

8 3 8 . 2 8 3 8 . 2 8 3 8 . 2 8 3 8 . 3 8 3 8 . 3

8 3 8 . 3 8 3 8 . 4 8 3 8 . 4 8 3 8 . 5 8 3 8 . 5

8 3 8 . 5 8 3 8 . 6 8 3 8 . 6 8 3 8 . 6 8 3 8 . 7

8 3 8 . 7 8 3 8 . 7 8 3 8 . 8 8 3 8 . 8 8 3 8 . 8

8 3 8 . 9 8 3 8 . 9 8 3 9 . O 8 3 9 . O 8 3 9 . O

8 3 9 . 1 8 3 9 . 1 8 3 9 . 1 8 3 9 . 2 8 3 9 . 2

8 3 9 . 2 8 3 9 . 3 8 3 9 . 3 8 3 9 . 3 8 3 9 . 4

8 3 9 . 4 8 3 9 . 5 8 3 9 . 5 8 3 9 . 5 8 3 9 . 6

8 3 9 . 6 8 3 9 . 6 8 3 9 . 7 8 3 9 . 7 8 3 9 . 7

8 3 9 . 8

8 3 8 . 1 8 3 8 . 1 8 3 8 . 2 8 3 8 . 2 8 3 8 . 2

8 3 8 . 3 8 3 8 . 3 8 3 8 . 3 8 3 8 . 4 8 3 8 . 4

8 3 8 . 4 8 3 8 . 5 8 3 8 . 5 8 3 8 . 6 8 3 8 . 6

8 3 8 . 6 8 3 8 . 7 8 3 8 . 7 8 3 8 . 7 8 3 8 . 8

8 3 8 . 8 8 3 8 . 8 8 3 8 . 9 8 3 8 . 9 8 3 8 . 9

8 3 9 . O 8 3 9 . O 8 3 9 . 1 8 3 9 . 1 8 3 9 . 1

8 3 9 . 2 8 3 9 . 2 8 3 9 . 2 8 3 9 . 3 8 3 9 . 3

8 3 9 . 3 8 3 9 . 4 8 3 9 . 4 8 3 9 . 4 8 3 9 . 5

8 3 9 . 5 8 3 9 . 6 8 3 9 . 6 8 3 9 . 6 8 3 9 . 7

8 3 9 . 7 8 3 9 . 7 8 3 9 . 8 8 3 9 . 8 8 3 9 . 8

8 3 9 . 9

8 3 8 . 2 8 3 8 . 2 8 3 8 . 3 8 3 8 . 3 8 3 8 . 3

8 3 8 . 4 8 3 8 . 4 8 3 8 . 4 8 3 8 . 5 8 3 8 . 5

8 3 8 . 5 8 3 8 . 6 8 3 8 . 6 8 3 8 . 7 8 3 8 . 7

8 3 8 . 7 8 3 8 . 8 8 3 8 . 8 8 3 8 . 8 8 3 8 . 9

8 3 8 . 9 8 3 8 . 9 8 3 9 . O 8 3 9 . O 8 3 9 . O

8 3 9 . 1 8 3 9 . 1 8 3 9 . 2 8 3 9 . 2 8 3 9 . 2

8 3 9 . 3 8 3 9 . 3 8 3 9 . 3 8 3 9 . 4 8 3 9 . 4

8 3 9 . 4 8 3 9 . 5 8 3 9 . 5 8 3 9 . 5 8 3 9 . 6

8 3 9 . 6 8 3 9 . 7 8 3 9 . 7 8 3 9 . 7 8 3 9 . 8

8 3 9 . 8 8 3 9 . 8 8 3 9 . 9 8 3 9 . 9 8 3 9 . 9

8 4 0 . O

8 3 8 . 3 8 3 8 . 3 8 3 8 . 4 8 3 8 . 4 8 3 8 . 4

8 3 8 . 5 8 3 8 . 5 8 3 8 . 5 8 3 8 . 6 8 3 8 . 6

8 3 8 . 6 8 3 8 . 7 8 3 8 . 7 8 3 8 . 8 8 3 8 . 8

8 3 8 . 8 8 3 8 . 9 8 3 8 . 9 8 3 8 . 9 8 3 9 . O

8 3 9 . O 8 3 9 . O 8 3 9 . 1 8 3 9 . 1 8 3 9 . 1

8 3 9 . 2 8 3 9 . 2 8 3 9 . 3 8 3 9 . 3 8 3 9 . 3

8 3 9 . 4 8 3 9 . 4 8 3 9 . 4 8 3 9 . 5 8 3 9 . 5

8 3 9 . 5 8 3 9 . 6 8 3 9 . 6 8 3 9 . 6 8 3 9 . 7

8 3 9 . 7 8 3 9 . 8 8 3 9 . 8 8 3 9 . 8 8 3 9 . 9

8 3 9 . 9 8 3 9 . 9 8 4 0 . O 8 4 0 . O 8 4 0 . O

8 4 0 . 1

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 3 5 . 1 5 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 3 5 . 3 5 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 3 5 . 5 5 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 3 5 . 8 5 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.19 Instructions to Generate Tables 59D - Correction of Observed Density to Density at 20°C for Generalized Lubricating Oils



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:








--`,,`,,,-`-`,,`,,`,`,,`---


Table 59D. Correction of Observed Density to 20'C Base Density (Lube Oils) If hydrometer used to determine density, apply glass correction before entering table

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 3 5 . 1 5 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 3 5 . 3 5 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 3 5 . 5 5 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 3 5 . 8 5 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0




8 3 6 . 5 8 3 6 . 5 8 3 6 . 5 8 3 6 . 6 8 3 6 . 6

8 3 6 . 6 8 3 6 . 7 8 3 6 . 7 8 3 6 . 7 8 3 6 . 8

8 3 6 . 8 8 3 6 . 8 8 3 6 . 8 8 3 6 . 9 8 3 6 . 9

8 3 6 . 9 8 3 7 . O 8 3 7 . O 8 3 7 . O 8 3 7 . 1

8 3 7 . 1 8 3 7 . 1 8 3 7 . 2 8 3 7 . 2 8 3 7 . 2

8 3 7 . 3 8 3 7 . 3 8 3 7 . 3 8 3 7 . 4 8 3 7 . 4

8 3 7 . 4 8 3 7 . 5 8 3 7 . 5 8 3 7 . 5 8 3 7 . 5

8 3 7 . 6 8 3 7 . 6 8 3 7 . 6 8 3 7 . 7 8 3 7 . 7

8 3 7 . 7 8 3 7 . 8 8 3 7 . 8 8 3 7 . 8 8 3 7 . 9

8 3 7 . 9 8 3 7 . 9 8 3 8 . O 8 3 8 . O 8 3 8 . O

8 3 8 . 1

8 3 6 . 6 8 3 6 . 6 8 3 6 . 6 8 3 6 . 7 8 3 6 . 7

8 3 6 . 7 8 3 6 . 8 8 3 6 . 8 8 3 6 . 8 8 3 6 . 9

8 3 6 . 9 8 3 6 . 9 8 3 6 . 9 8 3 7 . O 8 3 7 . O

8 3 7 . O 8 3 7 . 1 8 3 7 . 1 8 3 7 . 1 8 3 7 . 2

8 3 7 . 2 8 3 7 . 2 8 3 7 . 3 8 3 7 . 3 8 3 7 . 3

8 3 7 . 4 8 3 7 . 4 8 3 7 . 4 8 3 7 . 5 8 3 7 . 5

8 3 7 . 5 8 3 7 . 6 8 3 7 . 6 8 3 7 . 6 8 3 7 . 6

8 3 7 . 7 8 3 7 . 7 8 3 7 . 7 8 3 7 . 8 8 3 7 . 8

8 3 7 . 8 8 3 7 . 9 8 3 7 . 9 8 3 7 . 9 8 3 8 . O

8 3 8 . O 8 3 8 . O 8 3 8 . 1 8 3 8 . 1 8 3 8 . 1

8 3 8 . 2

8 3 6 . 7 8 3 6 . 7 8 3 6 . 7 8 3 6 . 8 8 3 6 . 8

8 3 6 . 8 8 3 6 . 9 8 3 6 . 9 8 3 6 . 9 8 3 7 . O

8 3 7 . O 8 3 7 . O 8 3 7 . O 8 3 7 . 1 8 3 7 . 1

8 3 7 . 1 8 3 7 . 2 8 3 7 . 2 8 3 7 . 2 8 3 7 . 3

8 3 7 . 3 8 3 7 . 3 8 3 7 . 4 8 3 7 . 4 8 3 7 . 4

8 3 7 . 5 8 3 7 . 5 8 3 7 . 5 8 3 7 . 6 8 3 7 . 6

8 3 7 . 6 8 3 7 . 7 8 3 7 . 7 8 3 7 . 7 8 3 7 . 7

8 3 7 . 8 8 3 7 . 8 8 3 7 . 8 8 3 7 . 9 8 3 7 . 9

8 3 7 . 9 8 3 8 . O 8 3 8 . O 8 3 8 . O 8 3 8 . 1

8 3 8 . 1 8 3 8 . 1 8 3 8 . 2 8 3 8 . 2 8 3 8 . 2

8 3 8 . 3

8 3 6 . 8 8 3 6 . 8 8 3 6 . 8 8 3 6 . 9 8 3 6 . 9

8 3 6 . 9 8 3 7 . O 8 3 7 . O 8 3 7 . O 8 3 7 . 1

8 3 7 . 1 8 3 7 . 1 8 3 7 . 1 8 3 7 . 2 8 3 7 . 2

8 3 7 . 2 8 3 7 . 3 8 3 7 . 3 8 3 7 . 3 8 3 7 . 4

8 3 7 . 4 8 3 7 . 4 8 3 7 . 5 8 3 7 . 5 8 3 7 . 5

8 3 7 . 6 8 3 7 . 6 8 3 7 . 6 8 3 7 . 7 8 3 7 . 7

8 3 7 . 7 8 3 7 . 8 8 3 7 . 8 8 3 7 . 8 8 3 7 . 8

8 3 7 . 9 8 3 7 . 9 8 3 7 . 9 8 3 8 . O 8 3 8 . O

8 3 8 . O 8 3 8 . 1 8 3 8 . 1 8 3 8 . 1 8 3 8 . 2

8 3 8 . 2 8 3 8 . 2 8 3 8 . 3 8 3 8 . 3 8 3 8 . 3

8 3 8 . 4

8 3 6 . 9 8 3 6 . 9 8 3 6 . 9 8 3 7 . O 8 3 7 . O

8 3 7 . O 8 3 7 . 1 8 3 7 . 1 8 3 7 . 1 8 3 7 . 2

8 3 7 . 2 8 3 7 . 2 8 3 7 . 2 8 3 7 . 3 8 3 7 . 3

8 3 7 . 3 8 3 7 . 4 8 3 7 . 4 8 3 7 . 4 8 3 7 . 5

8 3 7 . 5 8 3 7 . 5 8 3 7 . 6 8 3 7 . 6 8 3 7 . 6

8 3 7 . 7 8 3 7 . 7 8 3 7 . 7 8 3 7 . 8 8 3 7 . 8

8 3 7 . 8 8 3 7 . 9 8 3 7 . 9 8 3 7 . 9 8 3 7 . 9

8 3 8 . O 8 3 8 . O 8 3 8 . O 8 3 8 . 1 8 3 8 . 1

8 3 8 . 1 8 3 8 . 2 8 3 8 . 2 8 3 8 . 2 8 3 8 . 3

8 3 8 . 3 8 3 8 . 3 8 3 8 . 4 8 3 8 . 4 8 3 8 . 4

8 3 8 . 5

8 3 7 . O 8 3 7 . O 8 3 7 . O 8 3 7 . 1 8 3 7 . 1

8 3 7 . 1 8 3 7 . 2 8 3 7 . 2 8 3 7 . 2 8 3 7 . 3

8 3 7 . 3 8 3 7 . 3 8 3 7 . 3 8 3 7 . 4 8 3 7 . 4

8 3 7 . 4 8 3 7 . 5 8 3 7 . 5 8 3 7 . 5 8 3 7 . 6

8 3 7 . 6 8 3 7 . 6 8 3 7 . 7 8 3 7 . 7 8 3 7 . 7

8 3 7 . 8 8 3 7 . 8 8 3 7 . 8 8 3 7 . 9 8 3 7 . 9

8 3 7 . 9 8 3 8 . O 8 3 8 . O 8 3 8 . O 8 3 8 . O

8 3 8 . 1 8 3 8 . 1 8 3 8 . 1 8 3 8 . 2 8 3 8 . 2

8 3 8 . 2 8 3 8 . 3 8 3 8 . 3 8 3 8 . 3 8 3 8 . 4

8 3 8 . 4 8 3 8 . 4 8 3 8 . 5 8 3 8 . 5 8 3 8 . 5

8 3 8 . 6

8 3 7 . 1 8 3 7 . 1 8 3 7 . 1 8 3 7 . 2 8 3 7 . 2

8 3 7 . 2 8 3 7 . 3 8 3 7 . 3 8 3 7 . 3 8 3 7 . 4

8 3 7 . 4 8 3 7 . 4 8 3 7 . 4 8 3 7 . 5 8 3 7 . 5

8 3 7 . 5 8 3 7 . 6 8 3 7 . 6 8 3 7 . 6 8 3 7 . 7

8 3 7 . 7 8 3 7 . 7 8 3 7 . 8 8 3 7 . 8 8 3 7 . 8

8 3 7 . 9 8 3 7 . 9 8 3 7 . 9 8 3 8 . O 8 3 8 . O

8 3 8 . O 8 3 8 . 1 8 3 8 . 1 8 3 8 . 1 8 3 8 . 1

8 3 8 . 2 8 3 8 . 2 8 3 8 . 2 8 3 8 . 3 8 3 8 . 3

8 3 8 . 3 8 3 8 . 4 8 3 8 . 4 8 3 8 . 4 8 3 8 . 5

8 3 8 . 5 8 3 8 . 5 8 3 8 . 6 8 3 8 . 6 8 3 8 . 6

8 3 8 . 7

OC

3 5 . 0 0 3 5 . 0 5 3 5 . 1 0 3 5 . 1 5 3 5 . 2 0

3 5 . 2 5 3 5 . 3 0 3 5 . 3 5 3 5 . 4 0 3 5 . 4 5

3 5 . 5 0 3 5 . 5 5 3 5 . 6 0 3 5 . 6 5 3 5 . 7 0

3 5 . 7 5 3 5 . 8 0 3 5 . 8 5 3 5 . 9 0 3 5 . 9 5

3 6 . 0 0 3 6 . 0 5 3 6 . 1 0 3 6 . 1 5 3 6 . 2 0

3 6 . 2 5 3 6 . 3 0 3 6 . 3 5 3 6 . 4 0 3 6 . 4 5

3 6 . 5 0 3 6 . 5 5 3 6 . 6 0 3 6 . 6 5 3 6 . 7 0

3 6 . 7 5 3 6 . 8 0 3 6 . 8 5 3 6 . 9 0 3 6 . 9 5

3 7 . 0 0 3 7 . 0 5 3 7 . 1 0 3 7 . 1 5 3 7 . 2 0

3 7 . 2 5 3 7 . 3 0 3 7 . 3 5 3 7 . 4 0 3 7 . 4 5

3 7 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.20 Instructions to Generate Table 60A - Correction of Volume to 20°C Against Density at 20°C for Generalized Crude Oils



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:



Increment temperature by 0.05?C in range of -50.00? to 150.00?C. Ensure that the temperature value remains rounded consistent with instructions in 11.1.5.4.

Determine the CTL using procedure in 1 1.1.7.1 & speciQing commodity group ?A.? Round the value for display consistent with instructions in 1 1.1.5.4.




--`,,`,,,-`-`,,`,,`,`,,`---


Table 60A. Volume Correction Factor Due to Temperature Against 20'C Base Density (Crude Oils)




4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0

O . 9 8 5 6 1 O . 9 8 5 5 7 O . 9 8 5 5 3 O . 9 8 5 5 0 O . 9 8 5 4 6

O . 9 8 5 4 2 O . 9 8 5 3 9 O . 9 8 5 3 5 O . 9 8 5 3 2 O . 9 8 5 2 8

O . 9 8 5 2 4 O . 9 8 5 2 1 O . 9 8 5 1 7 O . 9 8 5 1 4 O . 9 8 5 1 0

O . 9 8 5 0 6 O . 9 8 5 0 3 0 . 9 8 4 9 9 O . 9 8 4 9 5 O . 9 8 4 9 2

O . 9 8 4 8 8 O . 9 8 4 8 5 O . 9 8 4 8 1 O . 9 8 4 7 7 O . 9 8 4 7 4

O . 9 8 4 7 0 O . 9 8 4 6 7 O . 9 8 4 6 3 O . 9 8 4 5 9 O . 9 8 4 5 6

O . 9 8 4 5 2 O . 9 8 4 4 8 O . 9 8 4 4 5 O . 9 8 4 4 1 O . 9 8 4 3 8

O . 9 8 4 3 4 O . 9 8 4 3 0 O . 9 8 4 2 7 O . 9 8 4 2 3 O . 9 8 4 2 0

0 . 9 8 4 1 6 O . 9 8 4 1 2 O . 9 8 4 0 9 O . 9 8 4 0 5 O . 9 8 4 0 1

O . 9 8 3 9 8 O . 9 8 3 9 4 O . 9 8 3 9 1 O . 9 8 3 8 7 O . 9 8 3 8 3

O . 9 8 3 8 0

O . 9 8 5 6 1 O . 9 8 5 5 7 O . 9 8 5 5 4 O . 9 8 5 5 0 O . 9 8 5 4 6

O . 9 8 5 4 3 O . 9 8 5 3 9 O . 9 8 5 3 6 O . 9 8 5 3 2 O . 9 8 5 2 8

O . 9 8 5 2 5 O . 9 8 5 2 1 O . 9 8 5 1 7 O . 9 8 5 1 4 O . 9 8 5 1 0

O . 9 8 5 0 7 O . 9 8 5 0 3 0 . 9 8 4 9 9 0 . 9 8 4 9 6 O . 9 8 4 9 2

O . 9 8 4 8 9 O . 9 8 4 8 5 O . 9 8 4 8 1 O . 9 8 4 7 8 O . 9 8 4 7 4

O . 9 8 4 7 1 O . 9 8 4 6 7 O . 9 8 4 6 3 O . 9 8 4 6 0 O . 9 8 4 5 6

O . 9 8 4 5 2 0 . 9 8 4 4 9 O . 9 8 4 4 5 O . 9 8 4 4 2 O . 9 8 4 3 8

O . 9 8 4 3 4 O . 9 8 4 3 1 O . 9 8 4 2 7 O . 9 8 4 2 4 O . 9 8 4 2 0

0 . 9 8 4 1 6 O . 9 8 4 1 3 O . 9 8 4 0 9 O . 9 8 4 0 5 O . 9 8 4 0 2

O . 9 8 3 9 8 O . 9 8 3 9 5 O . 9 8 3 9 1 O . 9 8 3 8 7 O . 9 8 3 8 4

O . 9 8 3 8 0

O . 9 8 5 6 1 O . 9 8 5 5 8 O . 9 8 5 5 4 O . 9 8 5 5 0 O . 9 8 5 4 7

O . 9 8 5 4 3 O . 9 8 5 3 9 O . 9 8 5 3 6 O . 9 8 5 3 2 O . 9 8 5 2 9

O . 9 8 5 2 5 O . 9 8 5 2 1 O . 9 8 5 1 8 O . 9 8 5 1 4 O . 9 8 5 1 1

O . 9 8 5 0 7 O . 9 8 5 0 3 O . 9 8 5 0 0 0 . 9 8 4 9 6 O . 9 8 4 9 3

O . 9 8 4 8 9 O . 9 8 4 8 5 O . 9 8 4 8 2 O . 9 8 4 7 8 O . 9 8 4 7 4

O . 9 8 4 7 1 O . 9 8 4 6 7 O . 9 8 4 6 4 O . 9 8 4 6 0 O . 9 8 4 5 6

O . 9 8 4 5 3 0 . 9 8 4 4 9 0 . 9 8 4 4 6 O . 9 8 4 4 2 O . 9 8 4 3 8

O . 9 8 4 3 5 O . 9 8 4 3 1 O . 9 8 4 2 7 O . 9 8 4 2 4 O . 9 8 4 2 0

O . 9 8 4 1 7 O . 9 8 4 1 3 O . 9 8 4 0 9 O . 9 8 4 0 6 O . 9 8 4 0 2

O . 9 8 3 9 9 O . 9 8 3 9 5 O . 9 8 3 9 1 O . 9 8 3 8 8 O . 9 8 3 8 4

O . 9 8 3 8 1

O . 9 8 5 6 1 O . 9 8 5 5 8 O . 9 8 5 5 4 O . 9 8 5 5 1 O . 9 8 5 4 7

O . 9 8 5 4 3 O . 9 8 5 4 0 O . 9 8 5 3 6 O . 9 8 5 3 3 O . 9 8 5 2 9

O . 9 8 5 2 5 O . 9 8 5 2 2 O . 9 8 5 1 8 O . 9 8 5 1 5 O . 9 8 5 1 1

O . 9 8 5 0 7 O . 9 8 5 0 4 O . 9 8 5 0 0 0 . 9 8 4 9 6 O . 9 8 4 9 3

O . 9 8 4 8 9 O . 9 8 4 8 6 O . 9 8 4 8 2 O . 9 8 4 7 8 O . 9 8 4 7 5

O . 9 8 4 7 1 O . 9 8 4 6 8 O . 9 8 4 6 4 O . 9 8 4 6 0 O . 9 8 4 5 7

O . 9 8 4 5 3 O . 9 8 4 5 0 0 . 9 8 4 4 6 O . 9 8 4 4 2 O . 9 8 4 3 9

O . 9 8 4 3 5 O . 9 8 4 3 1 O . 9 8 4 2 8 O . 9 8 4 2 4 O . 9 8 4 2 1

O . 9 8 4 1 7 O . 9 8 4 1 3 O . 9 8 4 1 0 O . 9 8 4 0 6 O . 9 8 4 0 3

O . 9 8 3 9 9 O . 9 8 3 9 5 O . 9 8 3 9 2 O . 9 8 3 8 8 O . 9 8 3 8 4

O . 9 8 3 8 1

O . 9 8 5 6 2 O . 9 8 5 5 8 O . 9 8 5 5 5 O . 9 8 5 5 1 O . 9 8 5 4 7

O . 9 8 5 4 4 O . 9 8 5 4 0 O . 9 8 5 3 7 O . 9 8 5 3 3 O . 9 8 5 2 9

O . 9 8 5 2 6 O . 9 8 5 2 2 O . 9 8 5 1 8 O . 9 8 5 1 5 O . 9 8 5 1 1

O . 9 8 5 0 8 O . 9 8 5 0 4 O . 9 8 5 0 0 O . 9 8 4 9 7 O . 9 8 4 9 3

O . 9 8 4 9 0 O . 9 8 4 8 6 O . 9 8 4 8 2 0 . 9 8 4 7 9 O . 9 8 4 7 5

O . 9 8 4 7 2 O . 9 8 4 6 8 O . 9 8 4 6 4 O . 9 8 4 6 1 O . 9 8 4 5 7

O . 9 8 4 5 3 O . 9 8 4 5 0 0 . 9 8 4 4 6 O . 9 8 4 4 3 O . 9 8 4 3 9

O . 9 8 4 3 5 O . 9 8 4 3 2 O . 9 8 4 2 8 O . 9 8 4 2 5 O . 9 8 4 2 1

O . 9 8 4 1 7 O . 9 8 4 1 4 O . 9 8 4 1 0 O . 9 8 4 0 6 O . 9 8 4 0 3

O . 9 8 3 9 9 O . 9 8 3 9 6 O . 9 8 3 9 2 O . 9 8 3 8 8 O . 9 8 3 8 5

O . 9 8 3 8 1

O . 9 8 5 6 2 O . 9 8 5 5 8 O . 9 8 5 5 5 O . 9 8 5 5 1 O . 9 8 5 4 8

O . 9 8 5 4 4 O . 9 8 5 4 0 O . 9 8 5 3 7 O . 9 8 5 3 3 O . 9 8 5 3 0

O . 9 8 5 2 6 O . 9 8 5 2 2 O . 9 8 5 1 9 O . 9 8 5 1 5 O . 9 8 5 1 2

O . 9 8 5 0 8 O . 9 8 5 0 4 O . 9 8 5 0 1 O . 9 8 4 9 7 O . 9 8 4 9 4

O . 9 8 4 9 0 O . 9 8 4 8 6 O . 9 8 4 8 3 0 . 9 8 4 7 9 O . 9 8 4 7 5

O . 9 8 4 7 2 O . 9 8 4 6 8 O . 9 8 4 6 5 O . 9 8 4 6 1 O . 9 8 4 5 7

O . 9 8 4 5 4 O . 9 8 4 5 0 O . 9 8 4 4 7 O . 9 8 4 4 3 O . 9 8 4 3 9

O . 9 8 4 3 6 O . 9 8 4 3 2 O . 9 8 4 2 9 O . 9 8 4 2 5 O . 9 8 4 2 1

O . 9 8 4 1 8 O . 9 8 4 1 4 O . 9 8 4 1 0 O . 9 8 4 0 7 O . 9 8 4 0 3

O . 9 8 4 0 0 O . 9 8 3 9 6 O . 9 8 3 9 2 O . 9 8 3 8 9 O . 9 8 3 8 5

O . 9 8 3 8 2

O . 9 8 5 6 2 O . 9 8 5 5 9 O . 9 8 5 5 5 O . 9 8 5 5 2 O . 9 8 5 4 8

O . 9 8 5 4 4 O . 9 8 5 4 1 O . 9 8 5 3 7 O . 9 8 5 3 4 O . 9 8 5 3 0

O . 9 8 5 2 6 O . 9 8 5 2 3 O . 9 8 5 1 9 O . 9 8 5 1 5 O . 9 8 5 1 2

O . 9 8 5 0 8 O . 9 8 5 0 5 O . 9 8 5 0 1 O . 9 8 4 9 7 O . 9 8 4 9 4

O . 9 8 4 9 0 O . 9 8 4 8 7 O . 9 8 4 8 3 0 . 9 8 4 7 9 0 . 9 8 4 7 6

O . 9 8 4 7 2 O . 9 8 4 6 9 O . 9 8 4 6 5 O . 9 8 4 6 1 O . 9 8 4 5 8

O . 9 8 4 5 4 O . 9 8 4 5 1 O . 9 8 4 4 7 O . 9 8 4 4 3 O . 9 8 4 4 0

O . 9 8 4 3 6 O . 9 8 4 3 2 O . 9 8 4 2 9 O . 9 8 4 2 5 O . 9 8 4 2 2

O . 9 8 4 1 8 O . 9 8 4 1 4 O . 9 8 4 1 1 O . 9 8 4 0 7 O . 9 8 4 0 4

O . 9 8 4 0 0 O . 9 8 3 9 6 O . 9 8 3 9 3 O . 9 8 3 8 9 O . 9 8 3 8 6

O . 9 8 3 8 2

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.21 Instructions to Generate Table 60B - Correction of Volume to 20°C Against Density at 20°C for Generalized Products



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:








--`,,`,,,-`-`,,`,,`,`,,`---


Table 60B. Volume Correction Factor Due to Temperature Against 20'C Base Density (Refined Products)


OC

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0

Base Density (kg/m3) 925 . O 9 2 5 . 1 925 .2 9 2 5 . 3 925 .4

Volume Correction for the Effect of Temperature on

0 . 9 8 5 0 4 0 . 9 8 5 0 4 0 . 9 8 5 0 4 0 . 9 8 5 0 4 0 . 9 8 5 0 4 0 . 9 8 5 0 0 0 . 9 8 5 0 0 0 . 9 8 5 0 0 0 . 9 8 5 0 1 0 . 9 8 5 0 1 0 . 9 8 4 9 6 0 . 9 8 4 9 6 0 . 9 8 4 9 7 0 . 9 8 4 9 7 0 . 9 8 4 9 7 0 . 9 8 4 9 2 0 . 9 8 4 9 3 0 . 9 8 4 9 3 0 . 9 8 4 9 3 0 . 9 8 4 9 3 0 . 9 8 4 8 9 0 . 9 8 4 8 9 0 . 9 8 4 8 9 0 . 9 8 4 8 9 0 . 9 8 4 8 9

0 . 9 8 4 8 5 0 . 9 8 4 8 5 0 . 9 8 4 8 5 0 . 9 8 4 8 5 0 . 9 8 4 8 6 0 . 9 8 4 8 1 0 . 9 8 4 8 1 0 . 9 8 4 8 2 0 . 9 8 4 8 2 0 . 9 8 4 8 2 0 . 9 8 4 7 7 0 . 9 8 4 7 8 0 . 9 8 4 7 8 0 . 9 8 4 7 8 0 . 9 8 4 7 8 0 . 9 8 4 7 4 0 . 9 8 4 7 4 0 . 9 8 4 7 4 0 . 9 8 4 7 4 0 . 9 8 4 7 4 0 . 9 8 4 7 0 0 . 9 8 4 7 0 0 . 9 8 4 7 0 0 . 9 8 4 7 0 0 . 9 8 4 7 1

0 . 9 8 4 6 6 0 . 9 8 4 6 6 0 . 9 8 4 6 7 0 . 9 8 4 6 7 0 . 9 8 4 6 7 0 . 9 8 4 6 2 0 . 9 8 4 6 3 0 . 9 8 4 6 3 0 . 9 8 4 6 3 0 . 9 8 4 6 3 0 . 9 8 4 5 9 0 . 9 8 4 5 9 0 . 9 8 4 5 9 0 . 9 8 4 5 9 0 . 9 8 4 5 9 0 . 9 8 4 5 5 0 . 9 8 4 5 5 0 . 9 8 4 5 5 0 . 9 8 4 5 5 0 . 9 8 4 5 6 0 . 9 8 4 5 1 0 . 9 8 4 5 1 0 . 9 8 4 5 1 0 . 9 8 4 5 2 0 . 9 8 4 5 2

0 . 9 8 4 4 7 0 . 9 8 4 4 8 0 . 9 8 4 4 8 0 . 9 8 4 4 8 0 . 9 8 4 4 8 0 . 9 8 4 4 4 0 . 9 8 4 4 4 0 . 9 8 4 4 4 0 . 9 8 4 4 4 0 . 9 8 4 4 4 0 . 9 8 4 4 0 0 . 9 8 4 4 0 0 . 9 8 4 4 0 0 . 9 8 4 4 0 0 . 9 8 4 4 1 0 . 9 8 4 3 6 0 . 9 8 4 3 6 0 . 9 8 4 3 6 0 . 9 8 4 3 7 0 . 9 8 4 3 7 0 . 9 8 4 3 2 0 . 9 8 4 3 2 0 . 9 8 4 3 3 0 . 9 8 4 3 3 0 . 9 8 4 3 3

0 . 9 8 4 2 8 0 . 9 8 4 2 9 0 . 9 8 4 2 9 0 . 9 8 4 2 9 0 . 9 8 4 2 9 0 . 9 8 4 2 5 0 . 9 8 4 2 5 0 . 9 8 4 2 5 0 . 9 8 4 2 5 0 . 9 8 4 2 6 0 . 9 8 4 2 1 0 . 9 8 4 2 1 0 . 9 8 4 2 1 0 . 9 8 4 2 2 0 . 9 8 4 2 2 0 . 9 8 4 1 7 0 . 9 8 4 1 7 0 . 9 8 4 1 8 0 . 9 8 4 1 8 0 . 9 8 4 1 8 0 . 9 8 4 1 3 0 . 9 8 4 1 4 0 . 9 8 4 1 4 0 . 9 8 4 1 4 0 . 9 8 4 1 4

0 . 9 8 4 1 0 0 . 9 8 4 1 0 0 . 9 8 4 1 0 0 . 9 8 4 1 0 0 . 9 8 4 1 1 0 . 9 8 4 0 6 0 . 9 8 4 0 6 0 . 9 8 4 0 6 0 . 9 8 4 0 7 0 . 9 8 4 0 7 0 . 9 8 4 0 2 0 . 9 8 4 0 2 0 . 9 8 4 0 3 0 . 9 8 4 0 3 0 . 9 8 4 0 3 0 . 9 8 3 9 8 0 . 9 8 3 9 9 0 . 9 8 3 9 9 0 . 9 8 3 9 9 0 . 9 8 3 9 9 0 . 9 8 3 9 5 0 . 9 8 3 9 5 0 . 9 8 3 9 5 0 . 9 8 3 9 5 0 . 9 8 3 9 6

0 . 9 8 3 9 1 0 . 9 8 3 9 1 0 . 9 8 3 9 1 0 . 9 8 3 9 2 0 . 9 8 3 9 2 0 . 9 8 3 8 7 0 . 9 8 3 8 7 0 . 9 8 3 8 8 0 . 9 8 3 8 8 0 . 9 8 3 8 8 0 . 9 8 3 8 3 0 . 9 8 3 8 4 0 . 9 8 3 8 4 0 . 9 8 3 8 4 0 . 9 8 3 8 4 0 . 9 8 3 8 0 0 . 9 8 3 8 0 0 . 9 8 3 8 0 0 . 9 8 3 8 0 0 . 9 8 3 8 1 O . 9 8 3 7 6 O . 9 8 3 7 6 O . 9 8 3 7 6 O . 9 8 3 7 7 O . 9 8 3 7 7

0 . 9 8 3 7 2 0 . 9 8 3 7 2 0 . 9 8 3 7 3 0 . 9 8 3 7 3 0 . 9 8 3 7 3 0 . 9 8 3 6 8 0 . 9 8 3 6 9 0 . 9 8 3 6 9 0 . 9 8 3 6 9 0 . 9 8 3 6 9 0 . 9 8 3 6 5 0 . 9 8 3 6 5 0 . 9 8 3 6 5 0 . 9 8 3 6 5 0 . 9 8 3 6 6 O . 9 8 3 6 1 O . 9 8 3 6 1 O . 9 8 3 6 1 O . 9 8 3 6 2 O . 9 8 3 6 2 0 . 9 8 3 5 7 0 . 9 8 3 5 7 0 . 9 8 3 5 8 0 . 9 8 3 5 8 0 . 9 8 3 5 8

0 . 9 8 3 5 3 0 . 9 8 3 5 4 0 . 9 8 3 5 4 0 . 9 8 3 5 4 0 . 9 8 3 5 4 0 . 9 8 3 5 0 0 . 9 8 3 5 0 0 . 9 8 3 5 0 0 . 9 8 3 5 0 0 . 9 8 3 5 1 O . 9 8 3 4 6 O . 9 8 3 4 6 O . 9 8 3 4 6 O . 9 8 3 4 7 O . 9 8 3 4 7 0 . 9 8 3 4 2 0 . 9 8 3 4 2 0 . 9 8 3 4 3 0 . 9 8 3 4 3 0 . 9 8 3 4 3 0 . 9 8 3 3 8 0 . 9 8 3 3 9 0 . 9 8 3 3 9 0 . 9 8 3 3 9 0 . 9 8 3 3 9

0 . 9 8 3 3 5 0 . 9 8 3 3 5 0 . 9 8 3 3 5 0 . 9 8 3 3 5 0 . 9 8 3 3 5 0 . 9 8 3 3 1 0 . 9 8 3 3 1 0 . 9 8 3 3 1 0 . 9 8 3 3 1 0 . 9 8 3 3 2 0 . 9 8 3 2 7 0 . 9 8 3 2 7 0 . 9 8 3 2 7 0 . 9 8 3 2 8 0 . 9 8 3 2 8 0 . 9 8 3 2 3 0 . 9 8 3 2 3 0 . 9 8 3 2 4 0 . 9 8 3 2 4 0 . 9 8 3 2 4 0 . 9 8 3 1 9 0 . 9 8 3 2 0 0 . 9 8 3 2 0 0 . 9 8 3 2 0 0 . 9 8 3 2 0

0 . 9 8 3 1 6 0 . 9 8 3 1 6 0 . 9 8 3 1 6 0 . 9 8 3 1 6 0 . 9 8 3 1 7

9 2 5 . 5 9 2 5 . 6 OC

Liquid (CTL) to 20'C

O . 9 8 5 0 5 O . 9 8 5 0 5 O . 9 8 5 0 1 O . 9 8 5 0 1 O . 9 8 4 9 7 O . 9 8 4 9 7 O . 9 8 4 9 3 O . 9 8 4 9 4 O . 9 8 4 9 0 O . 9 8 4 9 0

O . 9 8 4 8 6 O . 9 8 4 8 6 O . 9 8 4 8 2 O . 9 8 4 8 2 0 . 9 8 4 7 8 0 . 9 8 4 7 9 O . 9 8 4 7 5 O . 9 8 4 7 5 O . 9 8 4 7 1 O . 9 8 4 7 1

0 . 9 8 4 6 7 0 . 9 8 4 6 7 0 . 9 8 4 6 3 0 . 9 8 4 6 4 0 . 9 8 4 6 0 0 . 9 8 4 6 0 O . 9 8 4 5 6 O . 9 8 4 5 6 O . 9 8 4 5 2 O . 9 8 4 5 2

0 . 9 8 4 4 8 0 . 9 8 4 4 9 O . 9 8 4 4 5 O . 9 8 4 4 5 O . 9 8 4 4 1 O . 9 8 4 4 1 O . 9 8 4 3 7 O . 9 8 4 3 7 O . 9 8 4 3 3 O . 9 8 4 3 4

O . 9 8 4 3 0 O . 9 8 4 3 0 O . 9 8 4 2 6 O . 9 8 4 2 6 O . 9 8 4 2 2 O . 9 8 4 2 2 0 . 9 8 4 1 8 0 . 9 8 4 1 9 O . 9 8 4 1 5 O . 9 8 4 1 5

O . 9 8 4 1 1 O . 9 8 4 1 1 O . 9 8 4 0 7 O . 9 8 4 0 7 O . 9 8 4 0 3 O . 9 8 4 0 4 O . 9 8 4 0 0 O . 9 8 4 0 0 O . 9 8 3 9 6 O . 9 8 3 9 6

O . 9 8 3 9 2 O . 9 8 3 9 2 O . 9 8 3 8 8 O . 9 8 3 8 9 O . 9 8 3 8 5 O . 9 8 3 8 5 O . 9 8 3 8 1 O . 9 8 3 8 1 O . 9 8 3 7 7 O . 9 8 3 7 7

O . 9 8 3 7 3 O . 9 8 3 7 3 O . 9 8 3 7 0 O . 9 8 3 7 0 O . 9 8 3 6 6 O . 9 8 3 6 6 O . 9 8 3 6 2 O . 9 8 3 6 2 O . 9 8 3 5 8 O . 9 8 3 5 8

O . 9 8 3 5 4 O . 9 8 3 5 5 O . 9 8 3 5 1 O . 9 8 3 5 1 O . 9 8 3 4 7 O . 9 8 3 4 7 O . 9 8 3 4 3 O . 9 8 3 4 3 O . 9 8 3 3 9 O . 9 8 3 4 0

O . 9 8 3 3 6 O . 9 8 3 3 6 O . 9 8 3 3 2 O . 9 8 3 3 2 O . 9 8 3 2 8 O . 9 8 3 2 8 O . 9 8 3 2 4 O . 9 8 3 2 5 O . 9 8 3 2 1 O . 9 8 3 2 1

O . 9 8 3 1 7 O . 9 8 3 1 7

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.22 Instructions to Generate Table 60D - Correction of Volume to 20°C Against Density at 20°C for Generalized Lubricating Oils



Step 1:

Step 2:

Step 3:

Step 4:

Step 5:








--`,,`,,,-`-`,,`,,`,`,,`---


Table 60D. Volume Correction Factor Due to Temperature Against 20'C Base Density (Lube Oils)




4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0

O . 9 8 6 3 5 O . 9 8 6 3 1 O . 9 8 6 2 8 O . 9 8 6 2 4 O . 9 8 6 2 1

O . 9 8 6 1 7 O . 9 8 6 1 4 O . 9 8 6 1 1 O . 9 8 6 0 7 O . 9 8 6 0 4

O . 9 8 6 0 0 O . 9 8 5 9 7 O . 9 8 5 9 3 O . 9 8 5 9 0 O . 9 8 5 8 7

O . 9 8 5 8 3 O . 9 8 5 8 0 O . 9 8 5 7 6 O . 9 8 5 7 3 O . 9 8 5 6 9

O . 9 8 5 6 6 O . 9 8 5 6 3 O . 9 8 5 5 9 O . 9 8 5 5 6 O . 9 8 5 5 2

O . 9 8 5 4 9 O . 9 8 5 4 5 O . 9 8 5 4 2 O . 9 8 5 3 9 O . 9 8 5 3 5

O . 9 8 5 3 2 O . 9 8 5 2 8 O . 9 8 5 2 5 O . 9 8 5 2 1 O . 9 8 5 1 8

O . 9 8 5 1 5 O . 9 8 5 1 1 O . 9 8 5 0 8 O . 9 8 5 0 4 O . 9 8 5 0 1

O . 9 8 4 9 7 O . 9 8 4 9 4 O . 9 8 4 9 1 O . 9 8 4 8 7 O . 9 8 4 8 4

O . 9 8 4 8 0 O . 9 8 4 7 7 O . 9 8 4 7 3 O . 9 8 4 7 0 O . 9 8 4 6 7

O . 9 8 4 6 3

O . 9 8 6 3 5 O . 9 8 6 3 1 O . 9 8 6 2 8 O . 9 8 6 2 4 O . 9 8 6 2 1

O . 9 8 6 1 8 O . 9 8 6 1 4 O . 9 8 6 1 1 O . 9 8 6 0 7 O . 9 8 6 0 4

O . 9 8 6 0 0 O . 9 8 5 9 7 O . 9 8 5 9 4 O . 9 8 5 9 0 O . 9 8 5 8 7

O . 9 8 5 8 3 O . 9 8 5 8 0 O . 9 8 5 7 6 O . 9 8 5 7 3 O . 9 8 5 7 0

O . 9 8 5 6 6 O . 9 8 5 6 3 O . 9 8 5 5 9 O . 9 8 5 5 6 O . 9 8 5 5 2

O . 9 8 5 4 9 O . 9 8 5 4 6 O . 9 8 5 4 2 O . 9 8 5 3 9 O . 9 8 5 3 5

O . 9 8 5 3 2 O . 9 8 5 2 8 O . 9 8 5 2 5 O . 9 8 5 2 2 O . 9 8 5 1 8

O . 9 8 5 1 5 O . 9 8 5 1 1 O . 9 8 5 0 8 O . 9 8 5 0 4 O . 9 8 5 0 1

O . 9 8 4 9 8 O . 9 8 4 9 4 O . 9 8 4 9 1 O . 9 8 4 8 7 O . 9 8 4 8 4

O . 9 8 4 8 0 O . 9 8 4 7 7 O . 9 8 4 7 4 O . 9 8 4 7 0 O . 9 8 4 6 7

O . 9 8 4 6 3

O . 9 8 6 3 5 O . 9 8 6 3 1 O . 9 8 6 2 8 O . 9 8 6 2 5 O . 9 8 6 2 1

O . 9 8 6 1 8 O . 9 8 6 1 4 O . 9 8 6 1 1 O . 9 8 6 0 7 O . 9 8 6 0 4

O . 9 8 6 0 1 O . 9 8 5 9 7 O . 9 8 5 9 4 O . 9 8 5 9 0 O . 9 8 5 8 7

O . 9 8 5 8 3 O . 9 8 5 8 0 O . 9 8 5 7 7 O . 9 8 5 7 3 O . 9 8 5 7 0

O . 9 8 5 6 6 O . 9 8 5 6 3 O . 9 8 5 5 9 O . 9 8 5 5 6 O . 9 8 5 5 3

O . 9 8 5 4 9 O . 9 8 5 4 6 O . 9 8 5 4 2 O . 9 8 5 3 9 O . 9 8 5 3 5

O . 9 8 5 3 2 O . 9 8 5 2 9 O . 9 8 5 2 5 O . 9 8 5 2 2 O . 9 8 5 1 8

O . 9 8 5 1 5 O . 9 8 5 1 1 O . 9 8 5 0 8 O . 9 8 5 0 5 O . 9 8 5 0 1

O . 9 8 4 9 8 O . 9 8 4 9 4 O . 9 8 4 9 1 O . 9 8 4 8 7 O . 9 8 4 8 4

O . 9 8 4 8 1 O . 9 8 4 7 7 O . 9 8 4 7 4 O . 9 8 4 7 0 O . 9 8 4 6 7

O . 9 8 4 6 3

O . 9 8 6 3 5 O . 9 8 6 3 2 O . 9 8 6 2 8 O . 9 8 6 2 5 O . 9 8 6 2 1

O . 9 8 6 1 8 O . 9 8 6 1 4 O . 9 8 6 1 1 O . 9 8 6 0 8 O . 9 8 6 0 4

O . 9 8 6 0 1 O . 9 8 5 9 7 O . 9 8 5 9 4 O . 9 8 5 9 0 O . 9 8 5 8 7

O . 9 8 5 8 4 O . 9 8 5 8 0 O . 9 8 5 7 7 O . 9 8 5 7 3 O . 9 8 5 7 0

O . 9 8 5 6 6 O . 9 8 5 6 3 O . 9 8 5 6 0 O . 9 8 5 5 6 O . 9 8 5 5 3

O . 9 8 5 4 9 O . 9 8 5 4 6 O . 9 8 5 4 2 O . 9 8 5 3 9 O . 9 8 5 3 6

O . 9 8 5 3 2 O . 9 8 5 2 9 O . 9 8 5 2 5 O . 9 8 5 2 2 O . 9 8 5 1 8

O . 9 8 5 1 5 O . 9 8 5 1 2 O . 9 8 5 0 8 O . 9 8 5 0 5 O . 9 8 5 0 1

O . 9 8 4 9 8 O . 9 8 4 9 5 O . 9 8 4 9 1 O . 9 8 4 8 8 O . 9 8 4 8 4

O . 9 8 4 8 1 O . 9 8 4 7 7 O . 9 8 4 7 4 O . 9 8 4 7 1 O . 9 8 4 6 7

O . 9 8 4 6 4

O . 9 8 6 3 5 O . 9 8 6 3 2 O . 9 8 6 2 8 O . 9 8 6 2 5 O . 9 8 6 2 1

O . 9 8 6 1 8 O . 9 8 6 1 5 O . 9 8 6 1 1 O . 9 8 6 0 8 O . 9 8 6 0 4

O . 9 8 6 0 1 O . 9 8 5 9 7 O . 9 8 5 9 4 O . 9 8 5 9 1 O . 9 8 5 8 7

O . 9 8 5 8 4 O . 9 8 5 8 0 O . 9 8 5 7 7 O . 9 8 5 7 3 O . 9 8 5 7 0

O . 9 8 5 6 7 O . 9 8 5 6 3 O . 9 8 5 6 0 O . 9 8 5 5 6 O . 9 8 5 5 3

O . 9 8 5 4 9 O . 9 8 5 4 6 O . 9 8 5 4 3 O . 9 8 5 3 9 O . 9 8 5 3 6

O . 9 8 5 3 2 O . 9 8 5 2 9 O . 9 8 5 2 6 O . 9 8 5 2 2 O . 9 8 5 1 9

O . 9 8 5 1 5 O . 9 8 5 1 2 O . 9 8 5 0 8 O . 9 8 5 0 5 O . 9 8 5 0 2

O . 9 8 4 9 8 O . 9 8 4 9 5 O . 9 8 4 9 1 O . 9 8 4 8 8 O . 9 8 4 8 4

O . 9 8 4 8 1 O . 9 8 4 7 8 O . 9 8 4 7 4 O . 9 8 4 7 1 O . 9 8 4 6 7

O . 9 8 4 6 4

O . 9 8 6 3 5 O . 9 8 6 3 2 O . 9 8 6 2 8 O . 9 8 6 2 5 O . 9 8 6 2 2

O . 9 8 6 1 8 O . 9 8 6 1 5 O . 9 8 6 1 1 O . 9 8 6 0 8 O . 9 8 6 0 4

O . 9 8 6 0 1 O . 9 8 5 9 8 O . 9 8 5 9 4 O . 9 8 5 9 1 O . 9 8 5 8 7

O . 9 8 5 8 4 O . 9 8 5 8 0 O . 9 8 5 7 7 O . 9 8 5 7 4 O . 9 8 5 7 0

O . 9 8 5 6 7 O . 9 8 5 6 3 O . 9 8 5 6 0 O . 9 8 5 5 7 O . 9 8 5 5 3

O . 9 8 5 5 0 O . 9 8 5 4 6 O . 9 8 5 4 3 O . 9 8 5 3 9 O . 9 8 5 3 6

O . 9 8 5 3 3 O . 9 8 5 2 9 O . 9 8 5 2 6 O . 9 8 5 2 2 O . 9 8 5 1 9

O . 9 8 5 1 5 O . 9 8 5 1 2 O . 9 8 5 0 9 O . 9 8 5 0 5 O . 9 8 5 0 2

O . 9 8 4 9 8 O . 9 8 4 9 5 O . 9 8 4 9 1 O . 9 8 4 8 8 O . 9 8 4 8 5

O . 9 8 4 8 1 O . 9 8 4 7 8 O . 9 8 4 7 4 O . 9 8 4 7 1 O . 9 8 4 6 7

O . 9 8 4 6 4

O . 9 8 6 3 5 O . 9 8 6 3 2 0 . 9 8 6 2 9 O . 9 8 6 2 5 O . 9 8 6 2 2

O . 9 8 6 1 8 O . 9 8 6 1 5 O . 9 8 6 1 1 O . 9 8 6 0 8 O . 9 8 6 0 5

O . 9 8 6 0 1 O . 9 8 5 9 8 O . 9 8 5 9 4 O . 9 8 5 9 1 O . 9 8 5 8 7

O . 9 8 5 8 4 O . 9 8 5 8 1 O . 9 8 5 7 7 O . 9 8 5 7 4 O . 9 8 5 7 0

O . 9 8 5 6 7 O . 9 8 5 6 4 O . 9 8 5 6 0 O . 9 8 5 5 7 O . 9 8 5 5 3

O . 9 8 5 5 0 O . 9 8 5 4 6 O . 9 8 5 4 3 O . 9 8 5 4 0 O . 9 8 5 3 6

O . 9 8 5 3 3 O . 9 8 5 2 9 O . 9 8 5 2 6 O . 9 8 5 2 2 O . 9 8 5 1 9

O . 9 8 5 1 6 O . 9 8 5 1 2 O . 9 8 5 0 9 O . 9 8 5 0 5 O . 9 8 5 0 2

O . 9 8 4 9 8 O . 9 8 4 9 5 O . 9 8 4 9 2 O . 9 8 4 8 8 O . 9 8 4 8 5

O . 9 8 4 8 1 O . 9 8 4 7 8 O . 9 8 4 7 4 O . 9 8 4 7 1 O . 9 8 4 6 8

O . 9 8 4 6 4

4 0 . 0 0 4 0 . 0 5 4 0 . 1 0 4 0 . 1 5 4 0 . 2 0

4 0 . 2 5 4 0 . 3 0 4 0 . 3 5 4 0 . 4 0 4 0 . 4 5

4 0 . 5 0 4 0 . 5 5 4 0 . 6 0 4 0 . 6 5 4 0 . 7 0

4 0 . 7 5 4 0 . 8 0 4 0 . 8 5 4 0 . 9 0 4 0 . 9 5

4 1 . 0 0 4 1 . 0 5 4 1 . 1 0 4 1 . 1 5 4 1 . 2 0

4 1 . 2 5 4 1 . 3 0 4 1 . 3 5 4 1 . 4 0 4 1 . 4 5

4 1 . 5 0 4 1 . 5 5 4 1 . 6 0 4 1 . 6 5 4 1 . 7 0

4 1 . 7 5 4 1 . 8 0 4 1 . 8 5 4 1 . 9 0 4 1 . 9 5

4 2 . 0 0 4 2 . 0 5 4 2 . 1 0 4 2 . 1 5 4 2 . 2 0

4 2 . 2 5 4 2 . 3 0 4 2 . 3 5 4 2 . 4 0 4 2 . 4 5

4 2 . 5 0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.23 Instructions to Generate Tables 6C & 24C - Volume Correction Factors for Individual and Special Applications Volume Correction to 60°F Against Thermal Expansion Coefficients at 60°F

Input Variables:

Output Variables:

60'F thermal expansion factor and temperature. Pressure set to O psig.

CTL at input temperature.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Hold pressure at O psig.

Increment 60'F thermal expansion coefficient by 0 . 1 ~ 1 0 - ~ OF-' in range of 230.0~10-~ to 930.0~10-~ OF-'. Ensure that the value remains rounded consistent with instructions in 1 1.1.5.4.


Determine the CTL values using the procedure in 1 1.1.6.1 & speciqing the special applications group "C." Round the CTL value consistent with instructions in 1 1.1.5.4.

Increment the value of the thermal expansion coefficient or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of thermal expansion factor and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


Table 6C.

OF O

90.0 90.1 90.2 90.3 90.4

90.5 90.6 90.7 90.8 90.9

91.0 91.1 91.2 91.3 91.4

91.5 91.6 91.7 91.8 91.9

92.0 92.1 92.2 92.3 92.4

92.5 92.6 92.7 92.8 92.9

93.0 93.1 93.2 93.3 93.4

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

94.5 94.6 94.7 94.8 94.9

Volume Correction Factor Due to Temperature for Individual and Special Applications


Base alpha-60, l/'F .O004700 0.0004701 0.0004702 0.0004703 0.0004704 0.0004705 0.0004706 OF


0.98584 0.98584 0.98583 0.98583 0.98583 0.98582 0.98582 90.0 0.98579 0.98579 0.98578 0.98578 0.98578 0.98578 0.98577 90.1 0.98574 0.98574 0.98574 0.98573 0.98573 0.98573 0.98573 90.2 0.98570 0.98569 0.98569 0.98569 0.98568 0.98568 0.98568 90.3 0.98565 0.98565 0.98564 0.98564 0.98564 0.98563 0.98563 90.4

0.98560 0.98560 0.98560 0.98559 0.98559 0.98559 0.98558 90.5 0.98555 0.98555 0.98555 0.98554 0.98554 0.98554 0.98554 90.6 0.98551 0.98550 0.98550 0.98550 0.98549 0.98549 0.98549 90.7 O. 98546 O. 98546 O. 98545 O. 98545 O. 98545 O. 98544 O. 98544 90.8 0.98541 0.98541 0.98541 0.98540 0.98540 0.98540 0.98539 90.9

0.98536 0.98536 0.98536 0.98535 0.98535 0.98535 0.98535 91.0 0.98532 0.98531 0.98531 0.98531 0.98530 0.98530 0.98530 91.1 O. 98527 O. 98527 O. 98526 O. 98526 O. 98526 O. 98525 O. 98525 91.2 0.98522 0.98522 0.98522 0.98521 0.98521 0.98521 0.98520 91.3 O. 98517 O. 98517 O. 98517 O. 98517 O. 98516 O. 98516 O. 98516 91.4

0.98513 0.98512 0.98512 0.98512 0.98511 0.98511 0.98511 91.5 0.98508 0.98508 0.98507 0.98507 0.98507 0.98506 0.98506 91.6 0.98503 0.98503 0.98503 0.98502 0.98502 0.98502 0.98501 91.7 0.98499 0.98498 0.98498 0.98498 0.98497 0.98497 0.98497 91.8 0.98494 0.98493 0.98493 0.98493 0.98492 0.98492 0.98492 91.9

0.98489 0.98489 0.98488 0.98488 0.98488 0.98487 0.98487 92.0 0.98484 0.98484 0.98484 0.98483 0.98483 0.98483 0.98482 92.1 0.98480 0.98479 0.98479 0.98479 0.98478 0.98478 0.98478 92.2 0.98475 0.98474 0.98474 0.98474 0.98473 0.98473 0.98473 92.3 0.98470 0.98470 0.98469 0.98469 0.98469 0.98468 0.98468 92.4

0.98465 0.98465 0.98465 0.98464 0.98464 0.98464 0.98463 92.5 0.98461 0.98460 0.98460 0.98460 0.98459 0.98459 0.98459 92.6 0.98456 0.98456 0.98455 0.98455 0.98455 0.98454 0.98454 92.7 0.98451 0.98451 0.98450 0.98450 0.98450 0.98449 0.98449 92.8 0.98446 0.98446 0.98446 0.98445 0.98445 0.98445 0.98444 92.9

0.98442 0.98441 0.98441 0.98441 0.98440 0.98440 0.98440 93.0 0.98437 0.98437 0.98436 0.98436 0.98436 0.98435 0.98435 93.1 0.98432 0.98432 0.98431 0.98431 0.98431 0.98430 0.98430 93.2 O. 98427 O. 98427 O. 98427 O. 98426 O. 98426 O. 98426 O. 98425 93.3 0.98423 0.98422 0.98422 0.98422 0.98421 0.98421 0.98421 93.4

O. 98418 O. 98413 O. 98408 O. 98404 O. 98399

O. 98394 O. 98389 O. 98385 O. 98380 O. 98375

O. 98418 O. 98413 O. 98408 O. 98403 O. 98399

O. 98394 O. 98389 O. 98384 O. 98380 O. 98375

O. 98417 O. 98412 O. 98408 O. 98403 O. 98398

O. 98393 O. 98389 O. 98384 O. 98379 O. 98374

O. 98417 O. 98412 O. 98407 O. 98403 O. 98398

O. 98393 O. 98388 O. 98384 O. 98379 O. 98374

O. 98417 O. 98412 O. 98407 O. 98402 O. 98398

O. 98393 O. 98388 O. 98383 O. 98379 O. 98374

0.98416 O. 98411 O. 98407 O. 98402 O. 98397

O. 98392 O. 98388 O. 98383 O. 98378 O. 98373

0.98416 O. 98411 O. 98406 O. 98402 O. 98397

O. 98392 O. 98387 O. 98383 O. 98378 O. 98373

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

0.98370 0.98370 0.98370 0.98369 0.98369 0.98369 0.98368 94.5 0.98366 0.98365 0.98365 0.98365 0.98364 0.98364 0.98364 94.6 0.98361 0.98361 0.98360 0.98360 0.98360 0.98359 0.98359 94.7 0.98356 0.98356 0.98356 0.98355 0.98355 0.98354 0.98354 94.8 0.98351 0.98351 0.98351 0.98350 0.98350 0.98350 0.98349 94.9

95.0 O. 98347 O. 98346 O. 98346 O. 98346 O. 98345 O. 98345 O. 98345 95.0



--`,,`,,,-`-`,,`,,`,`,,`---


Table 24C. Volume Correction Factor Due to Temperature to 60'F for Individual and Special Applications


Base alpha-60, l/'F "F 0.0004700 0.0004701 0.0004702 0.0004703 0.0004704 0.0004705 0.0004706 OF


90.0 0.98584 0.98584 0.98583 0.98583 0.98583 0.98582 0.98582 90.0 90.1 0.98579 0.98579 0.98578 0.98578 0.98578 0.98578 0.98577 90.1 90.2 0.98574 0.98574 0.98574 0.98573 0.98573 0.98573 0.98573 90.2 90.3 0.98570 0.98569 0.98569 0.98569 0.98568 0.98568 0.98568 90.3 90.4 0.98565 0.98565 0.98564 0.98564 0.98564 0.98563 0.98563 90.4

90.5 0.98560 0.98560 0.98560 0.98559 0.98559 0.98559 0.98558 90.5 90.6 0.98555 0.98555 0.98555 0.98554 0.98554 0.98554 0.98554 90.6 90.7 0.98551 0.98550 0.98550 0.98550 0.98549 0.98549 0.98549 90.7 90.8 O. 98546 O. 98546 O. 98545 O. 98545 O. 98545 O. 98544 O. 98544 90.8 90.9 0.98541 0.98541 0.98541 0.98540 0.98540 0.98540 0.98539 90.9

91.0 0.98536 0.98536 0.98536 0.98535 0.98535 0.98535 0.98535 91.0 91.1 0.98532 0.98531 0.98531 0.98531 0.98530 0.98530 0.98530 91.1 91.2 0.98527 0.98527 0.98526 0.98526 0.98526 0.98525 0.98525 91.2 91.3 0.98522 0.98522 0.98522 0.98521 0.98521 0.98521 0.98520 91.3 91.4 O. 98517 O. 98517 O. 98517 O. 98517 O. 98516 O. 98516 O. 98516 91.4

91.5 0.98513 0.98512 0.98512 0.98512 0.98511 0.98511 0.98511 91.5 91.6 0.98508 0.98508 0.98507 0.98507 0.98507 0.98506 0.98506 91.6 91.7 0.98503 0.98503 0.98503 0.98502 0.98502 0.98502 0.98501 91.7 91.8 0.98499 0.98498 0.98498 0.98498 0.98497 0.98497 0.98497 91.8 91.9 0.98494 0.98493 0.98493 0.98493 0.98492 0.98492 0.98492 91.9

92.0 0.98489 0.98489 0.98488 0.98488 0.98488 0.98487 0.98487 92.0 92.1 0.98484 0.98484 0.98484 0.98483 0.98483 0.98483 0.98482 92.1 92.2 0.98480 0.98479 0.98479 0.98479 0.98478 0.98478 0.98478 92.2 92.3 0.98475 0.98474 0.98474 0.98474 0.98473 0.98473 0.98473 92.3 92.4 0.98470 0.98470 0.98469 0.98469 0.98469 0.98468 0.98468 92.4

92.5 0.98465 0.98465 0.98465 0.98464 0.98464 0.98464 0.98463 92.5 92.6 0.98461 0.98460 0.98460 0.98460 0.98459 0.98459 0.98459 92.6 92.7 0.98456 0.98456 0.98455 0.98455 0.98455 0.98454 0.98454 92.7 92.8 0.98451 0.98451 0.98450 0.98450 0.98450 0.98449 0.98449 92.8 92.9 0.98446 0.98446 0.98446 0.98445 0.98445 0.98445 0.98444 92.9

93.0 0.98442 0.98441 0.98441 0.98441 0.98440 0.98440 0.98440 93.0 93.1 0.98437 0.98437 0.98436 0.98436 0.98436 0.98435 0.98435 93.1 93.2 0.98432 0.98432 0.98431 0.98431 0.98431 0.98430 0.98430 93.2 93.3 O. 98427 O. 98427 O. 98427 O. 98426 O. 98426 O. 98426 O. 98425 93.3 93.4 0.98423 0.98422 0.98422 0.98422 0.98421 0.98421 0.98421 93.4

93.5 0.98418 93.6 0.98413 93.7 0.98408 93.8 0.98404 93.9 0.98399

94.0 0.98394 94.1 0.98389 94.2 0.98385 94.3 0.98380 94.4 0.98375

O. 98418 O. 98413 O. 98408 O. 98403 O. 98399

O. 98394 O. 98389 O. 98384 O. 98380 O. 98375

O. 98417 O. 98412 O. 98408 O. 98403 O. 98398

O. 98393 O. 98389 O. 98384 O. 98379 O. 98374

O. 98417 O. 98412 O. 98407 O. 98403 O. 98398

O. 98393 O. 98388 O. 98384 O. 98379 O. 98374

O. 98417 O. 98412 O. 98407 O. 98402 O. 98398

O. 98393 O. 98388 O. 98383 O. 98379 O. 98374

0.98416 O. 98411 O. 98407 O. 98402 O. 98397

O. 98392 O. 98388 O. 98383 O. 98378 O. 98373

0.98416 O. 98411 O. 98406 O. 98402 O. 98397

O. 98392 O. 98387 O. 98383 O. 98378 O. 98373

93.5 93.6 93.7 93.8 93.9

94.0 94.1 94.2 94.3 94.4

94.5 0.98370 0.98370 0.98370 0.98369 0.98369 0.98369 0.98368 94.5 94.6 0.98366 0.98365 0.98365 0.98365 0.98364 0.98364 0.98364 94.6 94.7 0.98361 0.98361 0.98360 0.98360 0.98360 0.98359 0.98359 94.7 94.8 0.98356 0.98356 0.98356 0.98355 0.98355 0.98354 0.98354 94.8 94.9 0.98351 0.98351 0.98351 0.98350 0.98350 0.98350 0.98349 94.9

95. O O. 98347 O. 98346 O. 98346 O. 98346 O. 98345 O. 98345 O. 98345 95.0



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.24 Instructions to Generate Tables 54C & 60C - Volume Correction Factors for Individual and Special Applications Volume Correction to 15°C or 20°C Against Thermal Expansion Coefficients

Input Variables:

Output Variables:

60'F thermal expansion coefficient and temperature. Pressure set to O Wa (gauge).

CTL at input temperature.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Hold pressure at O Wa (gauge).

Increment 60'F thermal expansion coefficient by 0 . 2 ~ 1 0 - ~ OC-' in range of 414.0~10-~ to 1674~10-~ OC-'. Ensure that the value remains rounded consistent with instructions in 1 1.1.5.4.

Increment temperature by 0.05'F in range of -50.00" to 15O.OO'C. Ensure that the temperature value remains rounded consistent with instructions in 11.1.5.4.

Determine the CTL values using the procedure in 11.1.7.1 & speciQing the special applications group "C." Round the CTL value consistent with instructions in 11.1.5.4.

Increment the value of the thermal expansion coefficient or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of thermal expansion factor and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


Table 54C. Volume Correction Factor Due to Temperature to 15'C for Individual and Special Applications


Base alpha-60, l/'C "C 0.0009000 0.0009002 0.0009004 0.0009006 0.0009008 0.0009010 0.0009012 OC


35.00 35.05 35.10 35.15 35.20

35.25 35.30 35.35 35.40 35.45

35.50 35.55 35.60 35.65 35.70

35.75 35.80 35.85 35.90 35.95

36.00 36.05 36.10 36.15 36.20

36.25 36.30 36.35 36.40 36.45

36.50 36.55 36.60 36.65 36.70

36.75 36.80 36.85 36.90 36.95

37.00 37.05 37.10 37.15 37.20

37.25 37.30 37.35 37.40 37.45

37.50

O. 98192 O. 98187 O. 98182 O. 98178 O. 98173

O. 98169 O. 98164 O. 98160 O. 98155 O. 98151

0.98146 O. 98142 O. 98137 O. 98133 O. 98128

O. 98123 0.98119 O. 98114 O. 98110 O. 98105

O. 98101 O. 98096 O. 98092 O. 98087 O. 98083

O. 98078 O. 98073 O. 98069 O. 98064 O. 98060

O. 98055 O. 98051 O. 98046 O. 98042 O. 98037

O. 98032 O. 98028 O. 98023 O. 98019 O. 98014

O. 98010 O. 98005 O. 98001 0.97996 0.97992

O. 97987 O. 97982 0.97978 0.97973 0.97969

0.97964

O. 98191 O. 98187 O. 98182 O. 98178 O. 98173

O. 98168 O. 98164 O. 98159 O. 98155 O. 98150

0.98146 O. 98141 O. 98137 O. 98132 O. 98128

O. 98123 O. 98118 O. 98114 O. 98109 O. 98105

O. 98100 O. 98096 O. 98091 O. 98087 O. 98082

O. 98078 O. 98073 O. 98068 O. 98064 O. 98059

O. 98055 O. 98050 O. 98046 O. 98041 O. 98037

O. 98032 O. 98027 O. 98023 O. 98018 O. 98014

O. 98009 O. 98005 O. 98000 0.97996 0.97991

O. 97987 O. 97982 0.97977 0.97973 0.97968

0.97964

O. 98191 O. 98186 O. 98182 O. 98177 O. 98173

O. 98168 O. 98163 O. 98159 O. 98154 O. 98150

O. 98145 O. 98141 O. 98136 O. 98132 O. 98127

O. 98123 O. 98118 O. 98113 O. 98109 O. 98104

O. 98100 O. 98095 O. 98091 O. 98086 O. 98082

O. 98077 O. 98073 O. 98068 O. 98063 O. 98059

O. 98054 O. 98050 O. 98045 O. 98041 O. 98036

O. 98032 O. 98027 O. 98023 O. 98018 O. 98013

O. 98009 O. 98004 O. 98000 0.97995 0.97991

0.97986 O. 97982 0.97977 O. 97972 0.97968

0.97963

O. 98190 O. 98186 O. 98181 O. 98177 O. 98172

O. 98168 O. 98163 O. 98159 O. 98154 0.98149

O. 98145 O. 98140 O. 98136 O. 98131 O. 98127

O. 98122 O. 98118 O. 98113 O. 98109 O. 98104

O. 98099 O. 98095 O. 98090 O. 98086 O. 98081

O. 98077 O. 98072 O. 98068 O. 98063 O. 98058

O. 98054 O. 98049 O. 98045 O. 98040 O. 98036

O. 98031 O. 98027 O. 98022 O. 98018 O. 98013

O. 98008 O. 98004 0.97999 0.97995 0.97990

0.97986 O. 97981 0.97977 O. 97972 0.97967

0.97963

O. 98190 O. 98185 O. 98181 0.98176 O. 98172

O. 98167 O. 98163 O. 98158 O. 98154 0.98149

O. 98144 O. 98140 O. 98135 O. 98131 O. 98126

O. 98122 O. 98117 O. 98113 O. 98108 O. 98104

O. 98099 O. 98094 O. 98090 O. 98085 O. 98081

O. 98076 O. 98072 O. 98067 O. 98063 O. 98058

O. 98053 O. 98049 O. 98044 O. 98040 O. 98035

O. 98031 O. 98026 O. 98022 O. 98017 O. 98013

O. 98008 O. 98003 0.97999 0.97994 0.97990

O. 97985 O. 97981 0.97976 O. 97972 0.97967

0.97962

O. 98190 O. 98185 O. 98180 0.98176 O. 98171

O. 98167 0.98162 O. 98158 O. 98153 0.98149

O. 98144 O. 98140 O. 98135 O. 98130 O. 98126

O. 98121 O. 98117 O. 98112 O. 98108 O. 98103

O. 98099 O. 98094 O. 98089 O. 98085 O. 98080

O. 98076 O. 98071 O. 98067 O. 98062 O. 98058

O. 98053 O. 98049 O. 98044 O. 98039 O. 98035

O. 98030 O. 98026 O. 98021 O. 98017 O. 98012

O. 98008 O. 98003 0.97998 0.97994 0.97989

O. 97985 O. 97980 0.97976 0.97971 0.97967

0.97962

O. 98189 O. 98185 O. 98180 0.98176 O. 98171

O. 98166 0.98162 O. 98157 O. 98153 O. 98148

O. 98144 O. 98139 O. 98135 O. 98130 O. 98125

O. 98121 0.98116 O. 98112 O. 98107 O. 98103

O. 98098 O. 98094 O. 98089 O. 98084 O. 98080

O. 98075 O. 98071 O. 98066 O. 98062 O. 98057

O. 98053 O. 98048 O. 98044 O. 98039 O. 98034

O. 98030 O. 98025 O. 98021 O. 98016 O. 98012

O. 98007 O. 98003 0.97998 0.97993 0.97989

O. 97984 O. 97980 0.97975 0.97971 0.97966

0.97962

35.00 35.05 35.10 35.15 35.20

35.25 35.30 35.35 35.40 35.45

35.50 35.55 35.60 35.65 35.70

35.75 35.80 35.85 35.90 35.95

36.00 36.05 36.10 36.15 36.20

36.25 36.30 36.35 36.40 36.45

36.50 36.55 36.60 36.65 36.70

36.75 36.80 36.85 36.90 36.95

37.00 37.05 37.10 37.15 37.20

37.25 37.30 37.35 37.40 37.45

37.50



--`,,`,,,-`-`,,`,,`,`,,`---


Table 60C. Volume Correction Factor Due to Temperature to 20'C for Individual and Special Applications


Base alpha-60, l/'C "C 0.0009000 0.0009002 0.0009004 0.0009006 0.0009008 0.0009010 0.0009012 OC


35.00 35.05 35.10 35.15 35.20

35.25 35.30 35.35 35.40 35.45

35.50 35.55 35.60 35.65 35.70

35.75 35.80 35.85 35.90 35.95

36.00 36.05 36.10 36.15 36.20

36.25 36.30 36.35 36.40 36.45

36.50 36.55 36.60 36.65 36.70

36.75 36.80 36.85 36.90 36.95

37.00 37.05 37.10 37.15 37.20

37.25 37.30 37.35 37.40 37.45

37.50

O. 98636 O. 98631 O. 98627 O. 98622 O. 98618

O. 98613 O. 98608 O. 98604 O. 98599 O. 98595

O. 98590 O. 98586 O. 98581 O. 98576 O. 98572

O. 98567 O. 98563 O. 98558 O. 98554 O. 98549

O. 98544 O. 98540 O. 98535 O. 98531 O. 98526

O. 98522 O. 98517 O. 98513 O. 98508 O. 98503

0.98499 O. 98494 O. 98490 O. 98485 O. 98481

0.98476 O. 98471 O. 98467 0.98462 O. 98458

O. 98453 0.98449 O. 98444 O. 98439 O. 98435

O. 98430 O. 98426 O. 98421 O. 98417 O. 98412

O. 98407

O. 98635 O. 98631 0.98626 O. 98622 O. 98617

O. 98613 O. 98608 O. 98604 O. 98599 O. 98594

O. 98590 O. 98585 O. 98581 O. 98576 O. 98572

O. 98567 O. 98562 O. 98558 O. 98553 O. 98549

O. 98544 O. 98540 O. 98535 O. 98530 O. 98526

O. 98521 O. 98517 O. 98512 O. 98508 O. 98503

O. 98498 O. 98494 O. 98489 O. 98485 O. 98480

0.98476 O. 98471 O. 98467 0.98462 O. 98457

O. 98453 O. 98448 O. 98444 O. 98439 O. 98435

O. 98430 O. 98425 O. 98421 0.98416 O. 98412

O. 98407

O. 98635 O. 98631 0.98626 O. 98621 O. 98617

O. 98612 O. 98608 O. 98603 O. 98599 O. 98594

O. 98590 O. 98585 O. 98580 O. 98576 O. 98571

O. 98567 O. 98562 O. 98558 O. 98553 O. 98548

O. 98544 O. 98539 O. 98535 O. 98530 O. 98526

O. 98521 O. 98516 O. 98512 O. 98507 O. 98503

O. 98498 O. 98494 O. 98489 O. 98484 O. 98480

O. 98475 O. 98471 O. 98466 0.98462 O. 98457

O. 98452 O. 98448 O. 98443 O. 98439 O. 98434

O. 98430 O. 98425 O. 98420 0.98416 O. 98411

O. 98407

O. 98635 O. 98630 0.98626 O. 98621 O. 98617

O. 98612 O. 98607 O. 98603 O. 98598 O. 98594

O. 98589 O. 98585 O. 98580 O. 98575 O. 98571

O. 98566 O. 98562 O. 98557 O. 98553 O. 98548

O. 98544 O. 98539 O. 98534 O. 98530 O. 98525

O. 98521 O. 98516 O. 98512 O. 98507 O. 98502

O. 98498 O. 98493 O. 98489 O. 98484 O. 98480

O. 98475 O. 98470 O. 98466 O. 98461 O. 98457

O. 98452 O. 98448 O. 98443 O. 98438 O. 98434

O. 98429 O. 98425 O. 98420 0.98416 O. 98411

O. 98406

O. 98635 O. 98630 O. 98625 O. 98621 0.98616

O. 98612 O. 98607 O. 98603 O. 98598 O. 98593

O. 98589 O. 98584 O. 98580 O. 98575 O. 98571

O. 98566 O. 98561 O. 98557 O. 98552 O. 98548

O. 98543 O. 98539 O. 98534 O. 98529 O. 98525

O. 98520 O. 98516 O. 98511 O. 98507 O. 98502

O. 98497 O. 98493 O. 98488 O. 98484 0.98479

O. 98475 O. 98470 O. 98465 O. 98461 O. 98456

O. 98452 O. 98447 O. 98443 O. 98438 O. 98433

O. 98429 O. 98424 O. 98420 O. 98415 O. 98411

O. 98406

O. 98634 O. 98630 O. 98625 O. 98621 0.98616

O. 98611 O. 98607 O. 98602 O. 98598 O. 98593

O. 98589 O. 98584 O. 98579 O. 98575 O. 98570

O. 98566 O. 98561 O. 98557 O. 98552 O. 98547

O. 98543 O. 98538 O. 98534 O. 98529 O. 98525

O. 98520 O. 98515 O. 98511 O. 98506 O. 98502

O. 98497 O. 98493 O. 98488 O. 98483 0.98479

O. 98474 O. 98470 O. 98465 O. 98461 O. 98456

O. 98451 O. 98447 O. 98442 O. 98438 O. 98433

O. 98429 O. 98424 0.98419 O. 98415 O. 98410

O. 98406

O. 98634 0.98629 O. 98625 O. 98620 0.98616

O. 98611 O. 98607 O. 98602 O. 98597 O. 98593

O. 98588 O. 98584 O. 98579 O. 98575 O. 98570

O. 98565 O. 98561 O. 98556 O. 98552 O. 98547

O. 98543 O. 98538 O. 98533 O. 98529 O. 98524

O. 98520 O. 98515 O. 98511 O. 98506 O. 98501

O. 98497 O. 98492 O. 98488 O. 98483 0.98479

O. 98474 O. 98469 O. 98465 O. 98460 O. 98456

O. 98451 0.98446 O. 98442 O. 98437 O. 98433

O. 98428 O. 98424 0.98419 O. 98414 O. 98410

O. 98405

35.00 35.05 35.10 35.15 35.20

35.25 35.30 35.35 35.40 35.45

35.50 35.55 35.60 35.65 35.70

35.75 35.80 35.85 35.90 35.95

36.00 36.05 36.10 36.15 36.20

36.25 36.30 36.35 36.40 36.45

36.50 36.55 36.60 36.65 36.70

36.75 36.80 36.85 36.90 36.95

37.00 37.05 37.10 37.15 37.20

37.25 37.30 37.35 37.40 37.45

37.50



--`,,`,,,-`-`,,`,,`,`,,`---


11.1.8.25 Instructions to Generate 1984 Chapter 11.2.1 Compressibility Factor Table - Compressibility Factors for Hydrocarbons Related to API Gravity and Metering Temperature

Input Variables: Base API gravity and temperature. Pressure set to O psig.

Output Variables: Fp at input temperature.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Hold pressure at O psig.

Increment base M I gravity value by 0.1'MI in range of -10.0" to 100.O'MI. Ensure that the observed M I gravity value remains rounded consistent with instructions in 1 1.1.5.4.

Increment temperature by O. 1°C in range of -58.0' to 302.O'F. Ensure that the temperature value remains rounded consistent with instructions in 1 1.1.5.4.

Determine the Fp values using the procedure in 1 1.1.6.1. Any commodity group can be specified. Round the Fp value consistent with instructions in 1 1.1.5.4.

Increment the value of the thermal expansion factor or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of M I gravity and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


(1981) Chapter 11.2.1 Table. Compressibility Factor Against API Gravity at 60'F

OF

135. O 135.1 135.2 135.3 135.4 135.5 135.6 135.7 135.8 135.9

136. O 136.1 136.2 136.3 136.4 136.5 136.6 136.7 136.8 136.9

137. O 137.1 137.2 137.3 137.4 137.5 137.6 137.7 137.8 137.9

138. O 138.1 138.2 138.3 138.4 138.5 138.6 138.7 138.8 138.9

139. O 139.1 139.2 139.3 139.4 139.5 139.6 139.7 139.8 139.9

140. O

65.0

1.179 1.179 1.180 1.180 1.181 1.181 1.182 1.182 1.183 1.184

1.184 1.185 1.185 1.186 1.186 1.187 1.187 1.188 1.188 1.189

1.190 1.190 1.191 1.191 1.192 1.192 1.193 1.193 1.194 1.195

1.195 1.196 1.196 1.197 1.197 1.198 1.198 1.199 1.200 1.200

1.201 1.201 1.202 1.202 1.203 1.203 1.204 1.205 1.205 1.206

1.206


Base API Gravity 65.1 65.2 65.3 65.4 65.5

Scaled Compressibility Factor (Fp), l/psig

1.181 1.182 1.182 1.183 1.183 1.184 1.184 1.185 1.186 1.186

1.187 1.187 1.188 1.188 1.189 1.189 1.190 1.191 1.191 1.192

1.192 1.193 1.193 1.194 1.194 1.195 1.196 1.196 1.197 1.197

1.198 1.198 1.199 1.199 1.200 1.201 1.201 1.202 1.202 1.203

1.203 1.204 1.204 1.205 1.206 1.206 1.207 1.207 1.208 1.208

1.209

1.184 1.184 1.185 1.185 1.186 1.187 1.187 1.188 1.188 1.189

1.189 1.190 1.190 1.191 1.191 1.192 1.193 1.193 1.194 1.194

1.195 1.195 1.196 1.196 1.197 1.198 1.198 1.199 1.199 1.200

1.200 1.201 1.201 1.202 1.203 1.203 1.204 1.204 1.205 1.205

1.206 1.207 1.207 1.208 1.208 1.209 1.209 1.210 1.210 1.211

1.212

1.186 1.187 1.187 1.188 1.189 1.189 1.190 1.190 1.191 1.191

1.192 1.192 1.193 1.194 1.194 1.195 1.195 1.196 1.196 1.197

1.197 1.198 1.199 1.199 1.200 1.200 1.201 1.201 1.202 1.202

1.203 1.204 1.204 1.205 1.205 1.206 1.206 1.207 1.207 1.208

1.209 1.209 1.210 1.210 1.211 1.211 1.212 1.213 1.213 1.214

1.214

1.189 1.190 1.190 1.191 1.191 1.192 1.192 1.193 1.193 1.194

1.194 1.195 1.196 1.196 1.197 1.197 1.198 1.198 1.199 1.199

1.200 1.201 1.201 1.202 1.202 1.203 1.203 1.204 1.205 1.205

1.206 1.206 1.207 1.207 1.208 1.208 1.209 1.210 1.210 1.211

1.211 1.212 1.212 1.213 1.214 1.214 1.215 1.215 1.216 1.216

1.217

1.192 1.192 1.193 1.193 1.194 1.194 1.195 1.195 1.196 1.197

1.197 1.198 1.198 1.199 1.199 1.200 1.200 1.201 1.202 1.202

1.203 1.203 1.204 1.204 1.205 1.205 1.206 1.207 1.207 1.208

1.208 1.209 1.209 1.210 1.211 1.211 1.212 1.212 1.213 1.213

1.214 1.214 1.215 1.216 1.216 1.217 1.217 1.218 1.218 1.219

1.220

65.6

1.194 1.195 1.195 1.196 1.196 1.197 1.197 1.198 1.199 1.199

1.200 1.200 1.201 1.201 1.202 1.203 1.203 1.204 1.204 1.205

1.205 1.206 1.206 1.207 1.208 1.208 1.209 1.209 1.210 1.210

1.211 1.212 1.212 1.213 1.213 1.214 1.214 1.215 1.215 1.216

1.217 1.217 1.218 1.218 1.219 1.219 1.220 1.221 1.221 1.222

1.222

135. O 135.1 135.2 135.3 135.4 135.5 135.6 135.7 135.8 135.9

136. O 136.1 136.2 136.3 136.4 136.5 136.6 136.7 136.8 136.9

137. O 137.1 137.2 137.3 137.4 137.5 137.6 137.7 137.8 137.9

138. O 138.1 138.2 138.3 138.4 138.5 138.6 138.7 138.8 138.9

139. O 139.1 139.2 139.3 139.4 139.5 139.6 139.7 139.8 139.9

140. O



--`,,`,,,-`-`,,`,,`,`,,`---


11 .I .8.26 Instructions to Generate 1984 Chapter 11.2.1 M Compressibility Factor Table - Compressibility Factors for Hydrocarbons Related to Density and Metering Temperature

Input Variables: Base 15’C density and temperature. Pressure set to O Wa (gauge).

Output Variables: Fp at input temperature.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Hold pressure at O Wa (gauge).

Increment base density value by 0.1 kg/m3 in range 61 1.2 to 1163.7 kg/m3. Ensure that the base density value remains rounded consistent with instructions in 1 1.1.5.4.


Determine the Fp values using the procedure in 1 1.1.7.1. Specifj the commodity type “A.” Round the Fp value consistent with instructions in 1 1.1.5.4.

Increment the value of the base density or temperature and return to Step 2 or 3 as appropriate. Continue until all combinations of density and temperature have been calculated.



--`,,`,,,-`-`,,`,,`,`,,`---


( 1 9 8 1 ) Chapter 11.2.1M Table. Compressibility Factor Against 15'C Base Density


OC

35 .00 3 5 . 0 5 35 .10 3 5 . 1 5 35 .20

3 5 . 2 5 35 .30 3 5 . 3 5 35 .40 3 5 . 4 5

35 .50 3 5 . 5 5 35 .60 3 5 . 6 5 35 .70

3 5 . 7 5 35 .80 3 5 . 8 5 35 .90 3 5 . 9 5

36 .00 3 6 . 0 5 36 .10 3 6 . 1 5 36 .20

3 6 . 2 5 36 .30 3 6 . 3 5 36 .40 3 6 . 4 5

36 .50 3 6 . 5 5 36 .60 3 6 . 6 5 36 .70

3 6 . 7 5 36 .80 3 6 . 8 5 36 .90 3 6 . 9 5

37 .00 3 7 . 0 5 37 .10 3 7 . 1 5 37 .20

3 7 . 2 5 37 .30 3 7 . 3 5 37 .40 3 7 . 4 5

37 .50

827 .0

O . 0883 O . 0883 O . 0883 O . 0884 O . 0884

O . 0884 O . 0884 O . 0885 O . 0885 O . 0885

O . 0886 O . 0886 O . 0886 O . 0886 O . 0887

O . 0887 O . 0887 O . 0888 O . 0888 O . 0888

O . 0888 O . 0889 O . 0889 O . 0889 O . 0890

O . 0890 O . 0890 O . 0890 O . 0891 O . 0891

O . 0891 O . 0892 O . 0892 O . 0892 O . 0892

O . 0893 O . 0893 O . 0893 O . 0894 O . 0894

O . 0894 O . 0894 O . 0895 O . 0895 O . 0895

O . 0896 O . 0896 O . 0896 O . 0896 O . 0897

O . 0897

Base Density (kg/m3) 8 2 7 . 1 827 .2 8 2 7 . 3

Scaled Compressibility Factor

827 .4 8 2 7 . 5 8 2 7 . 6

(FP), l/kPa (gauge)

O . 0882 O . 0883 O . 0883 O . 0883 O . 0884

O . 0884 O . 0884 O . 0884 O . 0885 O . 0885

O . 0885 O . 0886 O . 0886 O . 0886 O . 0886

O . 0887 O . 0887 O . 0887 O . 0888 O . 0888

O . 0888 O . 0888 O . 0889 O . 0889 O . 0889

O . 0890 O . 0890 O . 0890 O . 0890 O . 0891

O . 0891 O . 0891 O . 0892 O . 0892 O . 0892

O . 0892 O . 0893 O . 0893 O . 0893 O . 0893

O . 0894 O . 0894 O . 0894 O . 0895 O . 0895

O . 0895 O . 0895 O . 0896 O . 0896 O . 0896

O . 0897

O . 0882 O . 0882 O . 0883 O . 0883 O . 0883

O . 0884 O . 0884 O . 0884 O . 0884 O . 0885

O . 0885 O . 0885 O . 0886 O . 0886 O . 0886

O . 0886 O . 0887 O . 0887 O . 0887 O . 0887

O . 0888 O . 0888 O . 0888 O . 0889 O . 0889

O . 0889 O . 0889 O . 0890 O . 0890 O . 0890

O . 0891 O . 0891 O . 0891 O . 0891 O . 0892

O . 0892 O . 0892 O . 0893 O . 0893 O . 0893

O . 0893 O . 0894 O . 0894 O . 0894 O . 0895

O . 0895 O . 0895 O . 0895 O . 0896 O . 0896

O . 0896

O . 0882 O . 0882 O . 0882 O . 0883 O . 0883

O . 0883 O . 0884 O . 0884 O . 0884 O . 0884

O . 0885 O . 0885 O . 0885 O . 0885 O . 0886

O . 0886 O . 0886 O . 0887 O . 0887 O . 0887

O . 0887 O . 0888 O . 0888 O . 0888 O . 0889

O . 0889 O . 0889 O . 0889 O . 0890 O . 0890

O . 0890 O . 0891 O . 0891 O . 0891 O . 0891

O . 0892 O . 0892 O . 0892 O . 0893 O . 0893

O . 0893 O . 0893 O . 0894 O . 0894 O . 0894

O . 0895 O . 0895 O . 0895 O . 0895 O . 0896

O . 0896

O . 0882 O . 0882 O . 0882 O . 0882 O . 0883

O . 0883 O . 0883 O . 0883 O . 0884 O . 0884

O . 0884 O . 0885 O . 0885 O . 0885 O . 0885

O . 0886 O . 0886 O . 0886 O . 0887 O . 0887

O . 0887 O . 0887 O . 0888 O . 0888 O . 0888

O . 0889 O . 0889 O . 0889 O . 0889 O . 0890

O . 0890 O . 0890 O . 0891 O . 0891 O . 0891

O . 0891 O . 0892 O . 0892 O . 0892 O . 0893

O . 0893 O . 0893 O . 0893 O . 0894 O . 0894

O . 0894 O . 0895 O . 0895 O . 0895 O . 0895

O . 0896

O . 0881 O . 0881 O . 0882 O . 0882 O . 0882

O . 0883 O . 0883 O . 0883 O . 0883 O . 0884

O . 0884 O . 0884 O . 0885 O . 0885 O . 0885

O . 0885 O . 0886 O . 0886 O . 0886 O . 0887

O . 0887 O . 0887 O . 0887 O . 0888 O . 0888

O . 0888 O . 0889 O . 0889 O . 0889 O . 0889

O . 0890 O . 0890 O . 0890 O . 0890 O . 0891

O . 0891 O . 0891 O . 0892 O . 0892 O . 0892

O . 0892 O . 0893 O . 0893 O . 0893 O . 0894

O . 0894 O . 0894 O . 0894 O . 0895 O . 0895

O . 0895

O . 0881 O . 0881 O . 0881 O . 0882 O . 0882

O . 0882 O . 0883 O . 0883 O . 0883 O . 0883

O . 0884 O . 0884 O . 0884 O . 0885 O . 0885

O . 0885 O . 0885 O . 0886 O . 0886 O . 0886

O . 0887 O . 0887 O . 0887 O . 0887 O . 0888

O . 0888 O . 0888 O . 0888 O . 0889 O . 0889

O . 0889 O . 0890 O . 0890 O . 0890 O . 0890

O . 0891 O . 0891 O . 0891 O . 0892 O . 0892

O . 0892 O . 0892 O . 0893 O . 0893 O . 0893

O . 0894 O . 0894 O . 0894 O . 0894 O . 0895

O . 0895

OC

35 .00 3 5 . 0 5 35 .10 3 5 . 1 5 35 .20

3 5 . 2 5 35 .30 3 5 . 3 5 35 .40 3 5 . 4 5

35 .50 3 5 . 5 5 35 .60 3 5 . 6 5 35 .70

3 5 . 7 5 35 .80 3 5 . 8 5 35 .90 3 5 . 9 5

36 .00 3 6 . 0 5 36 .10 3 6 . 1 5 36 .20

3 6 . 2 5 36 .30 3 6 . 3 5 36 .40 3 6 . 4 5

36 .50 3 6 . 5 5 36 .60 3 6 . 6 5 36 .70

3 6 . 7 5 36 .80 3 6 . 8 5 36 .90 3 6 . 9 5

37 .00 3 7 . 0 5 37 .10 3 7 . 1 5 37 .20

3 7 . 2 5 37 .30 3 7 . 3 5 37 .40 3 7 . 4 5

37 .50



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Appendix A - History & Development of the 1980 Petroleum Measurement Tables

A.l Background

For the purpose of custody transfer of bulk petroleum oils and products, bulk volumes and contractual densities are stated at a specified standard or base temperature. 60°F is used as the base temperature within the United States and producing countries dealing with the United States. However, 15°C and 20°C are standard bases in many nations around the world. Volumes metered at temperatures other than base value are corrected to the base value by factors developed and tabulated in the Petroleum Measurement Tables.

The first joint tables for customary and metric units were developed in the late 1940s as described by Hall et al. ( 1975). Much of the data were based on the crude and fraction data published by Bearce and Peffer ( 19 16). These tables were published in 1952 as the result of close cooperation between the Institute of Petroleum (London), the Committee D-2 on Petroleum Products and Lubricants of the American Society for Testing Materials, and the American Petroleum Institute.

In 1972 Downer and Inkley demonstrated that the previously published tables were not satisfactorily applicable to many crude oils of current economic importance. The API and the National Bureau of Standards ( N B S ) initiated a cooperative venture, funded by the API, to create a data base of density measurements on both crude oils and refined products. This joint venture was initiated in 1974 and its intent was to provide the solid scientific base for the development of more accurate, consequently more equitable, measurement tables.

The completion of this five-year, $500,000 project in March 1979 opened the way for modernizing the tables. The sequence of events leading up to the publication of these tables is summarized in Table A-l. Using the NBS density data and taking advantage of publications of outstanding technical authorities, a Joint API-ASTM Subcommittee on Physical Properties produced the 1980 edition of the Petroleum Measurement Tables in close cooperation with the Institute of Petroleum. The results of this project are described in the open literature by Hankinson et al. (1979) and Hankinson et al. (1980).

Table A-2 gives a capsule picture of the issues that concerned the committee in producing the final version of its work.

A.2 Experimental Project

In the 1974 to 1979 program, API member companies provided the NBS with 463 samples; 21 1 of crude oils, the remainder of refined products. The list of samples represented 66.8 percent of the world crude production and 68.1 percent of the estimated reserves for 1974. The criteria for the selection of crude sample sources were (1) production for 1974, (2) estimated reserves for that year, and (3) countries wishing to contribute samples of national origin which did not fit the first two categories. Refined products were obtained primarily from API member companies. Each company was requested to submit at least three samples, preferably of those products having the highest refining volume. Refineries outside of the United States provided approximately 30 percent of the refined products samples.

A detailed description of the experimental technique and preliminary, unconfmed results were released by the NBS principal investigator, J. R Whetstone, in September 1978. Based on statistical studies performed by the Physical Properties Working Group and because of the group's recommendations, Whetstone checked approximately 30 percent of the original data and made significant modifications to the data base. In March 1979, Whetstone released the finalized data base to the API. Excluding samples on which fewer than three experimental measurements were reported, and certain duplicates, the final data base consisted of 349 samples distributed as shown in Table A-3. The data base contains temperature density data only and does not reflect viscosity, molecular weight, UOPK, or any additional characterization parameter. There were 25 samples for which fewer than three points of data were reported and 14 samples which were replicated for equipment calibration. The points in these two groups were eliminated from the data base, are not contained in Table A-3, and were not used in the correlation effort.



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A.3 Fluid Groups

The original NBS data were screened for consistency and to obtain a preliminary indication of the existence of more than a single population. The screening was performed by the use of linear equations and large machine generated plots (see Table A-4).

The samples included in the data base were identified by source and class of substance (crude oi1,jet fuel, kerosene, motor gasoline, fuel oil and lube oil). These classifications were used as a guide to statistical examination of the data base to determine if it contained identifiable, statistically different populations. It was found that there were five major identifiable groups of substances that had significantly different relationships between the coefficient of thermal expansion and density. The differences between each of these unusual groups and the rest of the data were all statistically significant. These deviations were attributed to differences in composition, aromaticity, density range, or other anomalies. These major and minor categories are identified in Table A-3.

A.4 Separate Representation Needed for Crude and Product Classes

Figure A-1 shows that the coefficient of thermal expansion of crude oil and the classes of products (gasolines, jet fuels, fuel oils, and lube oils) follow separate curves as a function of inverse density squared. This fact forces different representations to be used for each class in each of the new petroleum measurement tables. A more detailed breakdown of the product classifications is as follows:

Gasoline 50 < OAPI < 85 Jet fuels 37 < OAPI < 50 Fuel oils O<OAPI< 37 Lubricating oils O<OAPI< 45

It is worth emphasizing that meticulous care went into establishing, by both visual and mathematical analysis, the need for five populations of data, the crude and four product groups indicated. As stressed by William E. Deming, as early as 1939, "without a homogeneous population, a statistician's calculations by themselves, are an illusion, if not a delusion."

The most significant impact of this portion of the study was to demonstrate conclusively that the wide range of commercially important materials represented by the data base could not be adequately described by two dimensional tables, such as the previously published Tables 5 and 6 in the Petroleum Measurement Tables. The basic accuracy of this quality data would be destroyed and bias would be introduced by an attempt to characterize the five categories as a single group. This loss of accuracy and the introduction of bias is not defensible if the tables are to be equitable to all table users.

A S Correlation Development

The fundamental definition for the Coefficient of thermal expansion is:

1 dV V dt

a=--

where: a = coefficient of thermal expansion V = volume at any temperature.

The final form of the equation relating volume correction factors to easily obtainable measurements depends upon the integration of this definition. The integration, in turn, depends upon the assumptions made and the sequence in the derivation at which the assumptions are invoked.

A number of forms were proposed and studied by the working group. Three types of equations were eliminated from consideration:

1. forms with finite discontinuities in the equation or the derivative between temperatures of OOF and 300°F.



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2. equations containing complicated transcendental functions not suitable for general use on mini and microcomputers.

equations containing high order powers inside an exponential or other limitations prohibiting the use of single precision nonlinear analysis.

3.

From this type of elimination, an exponential equation emerged containing a second order term which exhibited the most desirable characteristics in terms of accuracy, simplicity, and curve shape. The working group accepted this exponential equation for use in the final correlation.

The equation was derived using:

where:

aT = a at the base temperature ß = a function of a and is independent of temperature.

Hence from Equations (A. 1) and (A.2):

dV - aT +ßAt V dt

A t = t - T

Which can be rearranged and integrated between t and T to give:

A study of the NBS data demonstrated that:

ß = k a T 2

where:

k = a temperature independent constant.

These equations were statistically validated by computer studies of the NBS data base. The precise value of k was selected from a consideration of (1) the computer studies, (2) the theoretical curvature of density with temperature, and (3) high temperature literature data on crudes, petroleum fractions, and Cg through C32 alkanes. These literature data were obtained from the work of Jessup (1929) and Orwall and Flory (1967). The value of k best expressing these criteria is 1.6.

Thus, Equation (A.5) becomes:

VCF=-=~=exp[-aTAt(l+O.SaTAt)] P T

where:

t = any temperature T =base temperature.

Equation (A.6) is valid for a particular fluid of known a T.



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It was determined that the coefficients of thermal expansion at the base temperature for each group are related to the densities at the base temperature by:

A.6 Parameter Determination and Results

The values of KO and Ki were established for each major group from a simultaneous nonlinear regression of all data points within that group to Equations (A.6) and (A.7). In this case the parameters were KO and Ki for the group and the vector of 60°F densities for each sample. See Column C of Table A-5.

The data were also reduced a set at a time by the use of Equation (A.6). In this case the parameters were the aT and p T for each sample. It is apparent that the use of two parameters for fitting a three or four point sample introduces a maximum bias because of the over specification of the degrees of freedom. These results are shown in Column A, Table A-5. The aT and p T pairs obtained from this procedure were, as the third method, fit to Equation (A.7) to determine the values of KO and Ki. See Column B of Table A-5.

The results and accuracy indicators are presented in Tables A-5 and A-6. Percent standard deviation given in the table is defined by:

where:

o = percent standard deviation pi = experimental density pc = calculated density np = number of points

no = total number of observations in a group.

An examination of Table A-5 shows that there is a significant increase in standard deviation between the data fit a set at a time (Column A) and the data fit simultaneously (Column C). This occurred for two major reasons:

1. By the act of grouping, which was necessary to produce a reasonable number of tables, sample differences such as composition, aromaticity, and density differences were averaged out. This effect could be reduced by the inclusion of some technique to characterize the aromaticity as described previously.

2. The reduction of the error in small data sets well below the experimental scatter of the data by fitting a set at a time. At this time there is insufficient information available to ascertain the distribution of the standard deviation between these two factors.

Table A-5 further shows that the simultaneous or global fit of all data in a group is significantly better than the attempt to generalize the pairs resulting from the set at a time regression. This is because of the scatter about Equation (A.7) caused by the "overfitting" of the small data sets. The global fit (Column C) gives equal weight to each data point while the generalization technique (Column B) gives equal weight to each data set, hence the global fit is a less biased, more equitable representation of the entire data base. The results from the global fit (see Table A- 6) were used in the preparation of the tables.

A complete set of results including the percent standard deviation, the maximum percent error, the density at 60°F, and the coefficient of thermal expansion are presented for each sample in the 1980 printed tables.



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Equation (A.6) presents the volume correction factor (VCF) as a function of the thermal expansion coefficient and density, both evaluated at the reference temperature. In that basic form, the equation is independent of any specific group and equally applicable to all groups. The equation is reliable over the temperature range of 0°F to 250°F and an API range of O" to 100". Equation (A.7) relates thermal expansion coefficient and density to a specific group through the constants KO and Ki for each group.

A.7 Development of 1980 Tables

Because of the growing importance of computers and their increasing influence on the metering effort, it was decided that the actual API Standard would consist of computer procedures. Subroutines were developed following these procedures so that identical answers were obtained regardless of the word size (within the limits of the word size conventions of the major hardware vendors) used by the hardware.

There were three common sets of tables in current use. These were in terms of "API (TABLES 5 and 6), relative density (TABLES 23 and 24), and density in kg/m3 (TABLES 53 and 54). In order to maximize accuracy and maintain convenience of use, three separate tables were required to replace each existing table. For example, for TABLE 6 there were: TABLE 6A Generalized Crude Oils, TABLE 6B Generalized Products, and TABLE 6C Volume Correction Factors for Individual and Special Applications. Equivalent tables were developed for the other two sets in the appropriate units. See Table A-7. The temperature ranges of the tables and the limits are shown in Table A-8.

The crude oil and products tables retained the format of the previously published tables. Volume correction factors or densities were tabulated as functions of temperature. These were computed from Equations (A.6) and (A.7) with the appropriate values for KO and Ki . Each products table was computed in three sections:

1. Fuel oils group equation from an API of O" to an API of 37".

2. Jet fuel group equation from an API of 37" to an API of 50".

3. Gasoline group equation from an API of 50" to an API of 85".

This is shown graphically in Figure A-2. TABLE 6A for crude oils covered a range from O" to 100"API.

TABLES Cy the Special Applications Tables, presented tabular entries of volume correction factor against thermal expansion coefficient and temperature. Each TABLE C was computed from Equation (A.6) and thus was independent of the group or substance. TABLE C could be used with any valid method of obtaining the thermal expansion coefficient for a given fluid as long as a statistically significant number of points were obtained. A minimum of ten such points was recommended. An appendix (see Volumes III, VI, and IB) to the published TABLES C presented values of the thermal expansion coefficient along with the base density for each of the NBS samples. In addition, values of the constants KO and Ki , were given for each major group. The existence of this table and its primary subroutine allowed the use of measured data for previously unstudied fluids to be easily incorporated into the procedure. High precision density data obtained from the laboratory for a fluid of interest could be reduced by Equation (A.l) to obtain aT and p T . TABLES C could then be entered with the aT so determined.

TABLES Cy when used with a minimum of ten data points, allowed one to extract the highest degree of accuracy from the data base. TABLES C introduced a high degree of flexibility into the procedure by allowing new data to be incorporated into the Standard. It was suggested that TABLES C be used when:

TABLES A and B did not adequately represent the thermal expansion properties of the fluids of interest; and

Precise thermal expansion coefficients could be obtained directly or indirectly by experiment (As an example, high precision density data may be used to compute the coefficient.); and

If buyers and sellers agree that, for their use, a greater degree of equity could be obtained.



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The lubricating oil samples were not fit satisfactorily by the new product tables. The API database consisted of 17 lube samples with 107 points over a density range of 861 to 940 kg/m3 and temperature range of 40" to 136°F. However, one of the samples had to be eliminated as unsuitable. Altogether the database did not contain a sufficient number of samples to develop a definitive equation. A request for further data for these specific sample types was made to the API by the Working Group. Two more sets of high quality data were made available. A combined database was formed consisting of 32 samples with 156 points covering a density range of 860 to 940 kg/m3 over a temperature range of 52" to 176°F. The resultant database was regressed using the same techniques as the original work. In 198 1 , the D Tables for Lubricating Oils became the first extension to the Standard.

A.8 Summary and Precision Statement

The 1980 tables gave factors for converting petroleum volumes observed at temperatures other than the base temperature to corresponding volumes at the base temperature for values of API gravity in the range O" to 100". The tables were based on density temperature determinations made by the U.S. National Bureau of Standards from 1974 to 1979 under contract to the API on 225 samples of products ranging from heavy fuel oil to gasoline blend components and 124 samples of crude oil that cover a wide range of quality and represent about 45 percent of the world's crude production and reserves as known during that time period. The thermal expansion properties (volume correction factors) for products (including lube stocks) and crude oils were correlated in separate, generalized tables as a function of temperature and density or API gravity. The predicted precision at the 95 percent confidence level was:

VCF precision at 95 % confidence level

Temperature 100°F 150°F 200°F 250°F

Crudes and Products +0.05% +O. 15% +0.25% +0.35%

A precision statement for the 250°F to 300°F portion of the tables was not given because it is an extrapolation.

Independent Test of the Correlation

In order to obtain an independent test of the revised tables, an oil of commercial importance which was not included in the NBS data set was studied. The steps of this study are described below.

1. An oil sample of Prudhoe Bay crude oil was supplied by SOHIO.

2. The experimental work was performed by Dr. James W.Gall of Phillips Petroleum Company.

a.

b.

3.

a.

b.

The sample was chilled to 50°F, settled and the upper portion siphoned off. This step removed any wax that formed at 50°F and the assorted solids in the original sample.

The oil densities were measured on a Mettler/ Paar high precision densitometer. The instrument was calibrated with both water and nitrogen at each temperature and pressure for which the oil density was measured. The calibration was confirmed using pentane.

The experimental results were tested against the new correlation by:

The constants for the thermal expansion coefficients equation were fured at the generalized values for crude oil.

KO = 341.0957 K, = 0.0

Weighting factors of unity were applied to the first five points of data since they are in the NBS data set temperature range. Weighting factors of 0.0001 were applied to the remaining four points. This step insured that the single parameter, the 60°F density, was not influenced by the data in the extrapolation region of the model.



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C. A nonlinear regression routine was used to fit the data to the TABLE 6 model and determine the missing parameter, the 60°F density.

The results are shown in Table A-9. The first five points of data were fit to a 0.0277 percent standard deviation; all points exhibit a 0.0365 percent standard deviation. These deviations are well within the 95 percent confidence limits given in the precision statement of the model and validate both the basic model and the temperature extrapolation.

A.9 Comparison of the Pre-1980 and 1980 Tables

The goal of the 1980 tables working group was to develop the revised tables based on the most recent data, not to be influenced by comparisons with the 1952 table. However, after the developmental effort was completed, a limited number of such comparisons were made for instructional purposes.

Figure A-3 shows the comparison of the volume correction factors of the 1952 and 1980 tables relative to the experimental data on the Prudhoe Bay crude. Table A-10 presents a representative sample of a comparison made between the NBS data and the 1952 TABLE 6.

Hydrometer Corrections

The hardcopy version of TABLES 5,23, and 53 include the appropriate stem correction for the thermal expansion of a glass hydrometer. These corrections are given by:

TABLES 5 and 23

HYC = 1.0 - 0.00001278(t - 60) - 0.0000000062(t - 60)2

t =OF

TABLE 53

HYC = 1.0 - 0.000023( t - 15) - 0.00000002(t - 1 5)2

t =OC

TABLE 59

t="C

The subroutines for these tables contain an override switch allowing the user to omit the correction. Such an override capability is necessary if the observed densities or gravities are obtained from an absolute densitometer rather than a temperature dependent hydrometer.

A.10 Density 8, Relative Density

The term "weight in air" is that weight which a quantity of fluid appears to have when weighed in air against commercial weights which have been standardized so that each will have a mass (weight in vacuo) equal to the nominal mass associated with it. The term "weight in vacuo" refers to the true mass of a fluid.

It should be noted that pure fluid densities as reported in the literature and which are used for the calibration of densitometers are based on "weight in vacuo." Hence, the densitometer readings obtained from such calibrations are also "in vacuo" values. The densities referred to in the 1980 Tables are all "in vacuo" values. Following the convention specified in 15.2.4.8 of API Publication 2564, Second Edition, and with the concurrence of the Institute of Petroleum, the term "specific gravity" was discontinued. It was replaced with the term "relative density." Relative density is a relationship defined by the ratios of the volume of fluid to the volume of water where both volumes are "in vacuo" values determined at identical temperatures.



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A . l l References

Bearce, H. W. and E. L. Peffer, "Technology Papers of the National Bureau of Standards-Density and Thermal Expansion of American Petroleum Oils," p. 125-154, GPO, Washington, D.C., 1916.

Deming, William E., ï ñ e o y of Sampling, John Wiley and Co., N.Y., N.Y., 1960.

Downer, L. and F. A. Inkley, Oil and Gas Journal, Vol. 10, No. 25, p. 52-55, June 19, 1972.

Hall, A. H., J. A. Simpson, and J. R Whetstone, "Investigation of Densities and Thermal Expansion Coefficients Applicable to Petroleum Measurement," SP 7 World Petroleum Congress, Tokyo, 1975.

Jessup, R.S., Journal ofReseUrch of the National Bureau of Standards, P. 985-101 1, 1929.

Orwall, R. A., and P. J. Flory, Journal ofAmerican Chemical SocieQ, 89:26, Dec. 1967.

Hankinson, R W., R. G. Segers, T. Krolikowski Buck, and F. P. Gielzecki, Oil and Gas Journal, Vol. 77, No. 52, p. 66-70, Dec. 24, 1979.

Hankinson, R W., R. G. Segers, T. Krolikowski Buck, and F. P. Gielzecki, Proceedings of the 59th Annual Gas Processors Association Convention, Houston, Texas, March 1980.



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Table A-I - API Thermal Volumetric Correction Factor Study

Downer and Inkley presented problem in 1972.

API sponsored five year NBS project to reaffm TABLES 5 and 6.

NBS produced density-temperature data for industry supplied samples.

NBS submitted data to API in September 1978 with revisions in March 1980

Preliminary results by NBS showed data did not confirm TABLES 5 and 6.

API COSM Physical Properties Working Group expanded October 1978.

Recommendations to API in March 1979.

API ballot on new tables issued

COSM, MARCH 1979-UNANIMOUS APPROVAL

COPM, AUGUST 1979-UNANIMOUS APPROVAL

IP, SEPTEMBER 1979-UNANIMOUS APPROVAL

Table A-2 - Issues Addressed by API Working Group

How should NBS data be screened for consistency?

Do the samples represent more than one statistical population?

What is the best equation for relating volume correction factor to temperature for a single population?

How should the density of a substance at base temperature be related to thermal expansion coefficients for a population of substances?

What is the best technique for extrapolating beyond 140°F, the limit of the NBS data?

How many tables should be published to replace the present tables?

What should be their limits, increments, and format?

How can universal computer code be best developed?



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Table A-3 API/NBS Data Base

Temperature Number of Number of Density Range Range

Category Samples Observations kg/m3 OF

Crude oil 1 24 600 770 - 990 40 - 133 Finished and unfinished 76 436 657 - 770 39 - 111 gasolines Jet fuels, kerosines, solvents Fuel oils, heating oils, diesel oils Lubricating oils Miscellaneous Lube Reformate, naphtha, etc. Jp-4 TOTALS

44 351 785 - 825 39 - 125

76 617 812 - 1075 39 - 136

17 107 861 - 940 40 - 136

2 13 927 - 972 50 - 127 6 43 664 - 823 39 - 129

4 21 736 - 763 41 - 104

349 2278

Table A 4 - Preliminary Study of NBS Data

Computer Generated Plots of Deviations in Densities from Linear Equations:

0 Screening of NBS Data for Anomalies

Large differences over small temperature ranges.

Same bias for points from several samples run on same day.

Bias in points run several months apart on same sample.

0 Visual Analysis of Total Population

Trends in deviations indicated if a sample was above, at, or below average, i.e. to identifj sub-groups in population.

Distinguish between data anomalies and trends.

0 Communicate Results

Data anomalies communicated to NBS (and others) who immediately recognized the problems.

Results

5 populations, 1 crude and 4 product groups indicated.

NBS revised data on nearly 30 percent of samples.



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Table A-5 - Comparison of Correlation Results

KO -i KIPT a, = P$

Tabular Entries in Percent Standard Deviation A B C From Method C

Grout, Generalization

n, n~ SetataTime of A Global Fit Ko Ki

Crude oils 124 690 .O152 .O371 .O253 341.0957 0.0 Gasoline and naphthas 76 436 .o 1 o9 .O304 .O266 192.4571 0.2438 Jet fuels and kerosines 44 351 .O 105 .O237 .O174 330.3010 0.0 Diesels, heating oils and 76 617 .O094 .O262 .O180 103.8720 0.2701 fuel oils Lubricating oils 17 107 .O067 .O274 .O197 144.04273 0.18964 TOTAL, 337 2201

Note: Alpha in reciprocal OF. Rho in kg/m3.

Table A-6 - Results of Global Regression of NBS Data to Final Equations

Percent Standard Group Number of Points Deviation

Crude oils 690 Gasolines 436 Jet fuels 351 Fuel oils 617 Lubricating oils 107

.O253

.O266

.O174

.O180

.O197

Table A-7 - 1980 Table Development

Tables

0 Three separate tables.

TABLE A Generalized Crude Oils (0- 100" API)

TABLE B Generalized Products (0-85' API)

TABLE C VCF for Individual and Special Applications

o Temperature and OAPI in 0.5 increments.

In Table A-5, the KO and Ki values for lubricating oils differ from those used in the published D Tables. This arises because further samples were submitted later to give a total data base of 32 samples and 156 points. Regression analysis of the revised database resulted in values for lubricating oils of KO = 0.0, Ki = 0.34878.



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0

0

0

Printout to five significant digits.

Interpolation not to be used.

Appendix to TABLE C contains p T and aT for each individual sample.

Table A-8 - 1980 Table Development

TABLE A TABLE B OAPI O F OAPI O F

0-40 0-300 0-40 0-300 40-50 0-250 40-50 0-250 50- 1 O0 0-200 50-85 0-200

Table A-9-Prudhoe Bay Oil Density (P = 24.8 psia)

Temperature Density, kg/m3

Percent OC O F Experimental Calculated Error

10.13 20.04 29.96 39.89 50.08 60.20 70.13 80.00 89.72

50.234 68.072 85.928 103.802 122.144 140.360 158.23 1 175.00 193.496

897.36 889.92 883.00 876.36 869.373 862.530 855.671 848.742 842.032

896.93 1 890.012 883.272 876.389 869.291 862.225 855.262 848.7 1 O

84 1.459

-.O477 .0225

.0309

.0033 -.O088 .0353

.O0478

.O0379 .0680

Average Absolute Percent Average Percent Standard Summary Error Deviation

1st 5 points .O2264 All points .O3759

.O277

.O365

p60 = 893.207 kg/m3



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Table A-IO-Average Error in the 1952 Table 6

Percent Over Actual at 60°F

Fluid 90°F 120°F 1 50°F

Crude oils 20OAPI 3OOAPI 4OOAPI

Products 20OAPI 4OOAPI 6OOAPI

0.01 0.04 0.09 0.07 0.16 0.26 0.09 0.2 1 0.32

0.06 0.14 0.25 0.04 0.1 1 0.18 0.19 0.4 1 0.62



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SECTION 1 - VOLUME CORRECTION FACTORS FOR CRUDE OILS. REFINED PRODUCTS. & LUBE OILS 20 1

400

Figure A-I - Coefficients of Expansion for Five Statistically Homogeneous Groups

-

900

I 1 I I I I

800

900

800

700

7

I 600 -

ln O

X 7

" 500

400

300

700

-

- -

- -

- I J I I

-

- -

- - 0API-37 48 52 85

I I I I I I

- I E. - 600

<o O T-

x c

500

0

GASOLINES

0



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0.4

0.3

Figure A-3 - Prudhoe Bay Crude August 1979 Data

TABLE 6 PREVIOUSLY PUBLISHED - ,cc --

1

-

-

I I I I I I I 40 60 80 1 O0 120 140 160 180 200

TEMPERATURE, O F



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Appendix B - History & Development of the 1981 Hydrocarbon Compressibility Factors

The compressibility standard (API Standard 1 101 , Appendix By Table 11) for hydrocarbons in the 0-90" API gravity ranges was developed in 1945 by Jacobson, et al. It was based on limited data obtained mostly on pure compounds and lubricating oil type materials. Also, Standard 1101 was developed without the aid of a mathematical model.

In 198 1 , a working group of the Committee on Static Petroleum Measurement was set up to revise the compressibility tables of Standard 1101. This group performed an extensive literature search and found only three sources of compressibility information. The resulting database was broader than that used in the previous standard, though. This standard replaced the discontinued Standard 1 1 O 1 , Appendix By Table II, 0- 1 00"API gravity portion. There were two versions of this 198 1 standard: Chapter 1 1.2.1 using customary units and Chapter 1 1.2.1M using metric units.

The database for this standard was obtained from Jessup, Downer and Gardiner, and Downer. It consisted of seven crude oils, five gasolines, and seven middle distillate-gas oils. The lubricating oil data from these sources were not included. Modeling results showed that lubricating oils are a different population than crude oils and other refined products. Their inclusion multiplies the compressibility correlation uncertainty by a factor of two. However, lubricating oils are not normally metered under pressure and do not require the use of this standard.

The limits of the experimental data are 20 to 76"API (934 to 681 kg/m3), 32 to 302°F (O to 15OoC), and O to 71 1 psig (O to 4902 kPa (gauge)). As a result of a Committee on Static Petroleum Measurement (COSM) and Committee on Petroleum Measurement (COPM) survey, the actual limits of the standard are broader: O to 90"API (1074 to 638 kg/m3), -20 to 200°F (-30 to 90°C), and O to 1500 psig (O to 10300 kPa (gauge)). Hence, certain portions of the standard represent extrapolated results. In these extrapolated regions, the uncertainty analysis may not be valid.

B.l

The basic mathematical model, used to develop this Standard, relates the compressibility factor exponentially to temperature and the square of molecular volume. Its form is:

Basic Mathematical Model & Uncertainty Analysis

A + B - T + - + - Pio Pio

where: F = compressibility factor T = temperature &o = density at 60°F.

(It is assumed that 1 / p60 is proportional to molecular volume.)

Here, compressibility is the result of the interaction of two molecular volumes and temperature. Equation íj3.1) is consistent with the development of the thermal expansion of hydrocarbons. The use of higher powers of T and &o

did not yield further significant minimization of compressibility factor uncertainty.

Using the above equation and database, maximum compressibility factor uncertainty is +6.5% at the 95% confidence level. Hence at worst, one should expect that the real compressibility factor for a given material could be either 6.5% higher or 6.5% lower than the value in the Standard. This statement is only true within the limits of the database. It may not be true for the extrapolated portions of the Standard.

To assess the possible uncertainty in the calculated volume at equilibrium pressure using the above database and equation, two approaches were taken. First it was assumed that only the correlation uncertainty in mean compressibility of +6.5% was significant. With this approach, volumetric uncertainties should be in the range of 0.02 to O. 1 O%, depending on operating conditions. These uncertainties are in agreement with the maximum error of O. 10% recommended by a COSM and CIPM survey.



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The first volumetric uncertainty analysis assumes that mean compressibility is not a function of pressure. For low pressures, this assumption is adequate. For higher pressures, mean compressibility will decrease with increasing pressure. At what pressure this effect becomes significant for the materials of this Standard is not definitely known. However, analysis of the Jessup data indicates that mean compressibility could possibly decrease by about 0.005% per psi (0.00073% per kPa) with increasing pressure. Incorporating both the compressibility correlation uncertainty and potential pressure uncertainty yields volumetric uncertainties in the range of 0.03 to 0.21%. Hence, the use of this Standard with operating pressures greater than the experimental limit of 71 1 psig (4902 kPa (gauge)) could double the uncertainty in calculated volume over the uncertainty based on available data.

B.2 References

Jacobsen, E. W., Ambrosius, E. E. Dashiell, J. W. , and Crawford, C. L., “Second Progress Report on Study of Existing Data on Compressibility of Liquid Hydrocarbons,” Report of the Central Committee on Pipe-Line Transportation, Vol. 2 (IV), p. 39-45, American Petroleum Institute, Washington, D.C., 1945.

Jessep, R. S. , “Compressibility and Thermal Expansion of Petroleum Oils in the Range O” to 300”C,” Bureau of Standards Journal of Research, Vol. 5, July to December 1930, p. 985-1039, National Bureau of Standards, Washington, D.C.

Downer, L., and Gardiner, K. E. S. , “Bulk Oil Measurement Compressibility Measurements on Crude Oils Deviations from API Standard 1101,” BP Research Report No. 20 5 8 7 M (8 pages), October 28, 1970.

Downer, L., “Bulk Oil Measurement Compressibility Data on Crude Oils and Petroleum Products Viewed as a Basis for Revised International Tables (API Standard 1101 Tables),” BP Research Report No. 20 639 (21 pages), January 17, 1972.



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Appendix C - Development of Modified CTL Equations for Base Temperatures Other Than 60" F

C.l Introduction

During the development of this revision of Chapter 1 1.1 , it became apparent that there was a need to examine the equations used to calculate the GL and allow for a base temperature other than 60°F for the following reasons:

0 The existing routines for base temperatures of 60°F, 15°C and 20°C did not always produce consistent results when VCFs were calculated to five, instead of four, decimal places.

0 The recognition of the differences between the IPTS-68 and ITS-90 temperature scales admits a slight difference in the definition of 60°F.

An attempt was made to devise a new, direct routine for the calculation of qL values for any base temperature other than 60°F (on an IPTS-68 basis). The objective was that the outputs using any base temperature should be consistent with those using the procedure for 60°F base temperature, i.e. equivalent inputs should produce equivalent outputs using either procedure.

This Appendix examines the feasibility of developing such a routine.

C.2 Changing Temperature Bases

There are three base temperatures in common use worldwide: 60°F, 15"C, and 20°C. When this Standard was being updated, there was a desire to directly use the metric densities and temperature units in the C, expression (Equation C.1) in such a way that consistent results would be obtained no matter the base temperature or units. It will be shown here that because of the pm (density at 60°F where 60°F is expressed on the IPTS-1968 temperature scale) used in equation (C.2) this set of GL expressions cannot be mathematically manipulated to directly use different base temperatures and still give consistent results. However, if a very accurate equation can be developed that directly gives pm given a density at some other base temperature, then this procedure can be used.

Changing to metric units and a metric base temperature requires the following:

0 Change the units of temperature and the thermal expansion coefficient used in Equations (C.l), and (C.2). Shifting the temperature values to an IPTS-68 basis and adding unit conversion parameters can easily do this.. This is discussed in subsection C.6 and in Appendix D.

0 Change Equation (C. 1) to use a base temperature other than 60°F. It can be shown that adding an extra term can correctly modify the equation to use any base temperature. When this is done, though, the same a60 value is still used for the CTL.

Even with these two changes, there is still the matter that the a60 correlation directly uses pm values. For the metric base temperatures, the desire is the use the 15°C or 20°C base density (p15 or p,) without the p60 value. This requires more than just scaling the coefficients in Equation (C.2). There is no direct mathematical translation to replace pm with these pis or p20 values. One way to eliminate the need for pm is to re-correlate the am expression to use the pis or p20 values. However, modifying the coefficients would introduce inconsistencies with the coefficients used for the non-metric methods based upon the 60°F standard. For this reason, this approach was rejected for the metric base temperatures.

The procedure that was developed for the metric tables requires firstly a calculation of the pm value, using an iterative approach as described in Appendix F.

The following sections describes the steps necessary to convert the GL equations based upon the 1980 Standard to equations that are capable of using any base temperature.



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C.3 Consistency of Results

One of the goals of this Standard is to provide consistent results when performing corrections using either metric or customary units. That is, when one corrects an observed density to the density at alternate conditions of temperature and pressure, the same result should be obtained irrespective of the base conditions used or the units in which they are expressed. The procedures adopted in this Standard ensure that consistency of results is always achieved.

For example, let us assume that we have a volume of oil with an observed density of 750.0 kg/m3 at 212°F (100°C) and 1 atm. We would like to correct this volume and density to 248°F (120°C) and 1 atm. We would like the corrected density and volume to be exactly the same whether we do the calculations in customary units using a 60°F standard density or metric units using a 15°C or 20°C standard density. Obviously, the GL values will be different since they account for corrections to the standard density. But the final resulting corrected density and volume must be the same.

Any modified CTL equation developed for metric temperatures had to produce results consistent with those given by the customary unit tables.

C.4 Original Equations

The original equation for the temperature correction factors contained in the 1980 Standard is:

where C,, is the correction factor for the temperature of the liquid, t is the alternate temperature (OF), p is the density at the alternate temperature (kg/m3), p60 is the density at the base temperature of 60°F (kg/m3), a60 is the thermal expansion coefficient at the base temperature of 60°F (OF-'), and At is the difference between the alternate temperature and the base temperature.

In the 1980 Standard, a60 was correlated to the p60 density by means of the equation:

There are several sets of coefficients for the a 6 0 thermal expansion coefficient (the KO , Ki , and K2 values) depending upon the liquid's commodity type classification and 60°F density.

The data used in the development of these equations were determined using instruments calibrated according to the IPTS-68 temperature scale.

C.5

For the metric tables, it is preferred to maintain the CTL equation in the form:

Mathematical Conversion from Customary to Metric Temperature Units

C, = = exp(-a, ( t - T)[1+ 0.8aT ( t - T)]) PT

where t and T are in "Cy T is the new base temperature and all calculations are directly based upon its value and the associated values of the density and thermal expansion coefficient at this temperature. The conversion of this equation is dependant on three main items:

C.5.1 Conversion of Temperatures

Note that, for simplicity, temperatures discussed in this section are expressed on the IPTS-68 temperature scale. The manipulations required to change from the IPTS-68 scale to the ITS-90 scale are described in C.6 and Appendix D.



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The first change to the CTL equation to use metric base conditions is to change the temperature units, from OF to OC. This is the easy part to accomplish. The temperature change for (t-T), At, only occurs as the product and this is dimensionless. The units of a60 are the reciprocal of the units of temperature, OF-'. So, if we change the units of At to OC and the units of a 6 0 to OC-', then nothing need be done to the GL equation. However, if we keep the units of a60 as OF-', then we need to use a term C,a,,At where C, takes care of any inconsistency of units between At and a 6 0 . This value will be:

(C-4) 9 C - -OFOC-' However, when a60 is expressed in OC-' then CT = l0CoC-' = 1

T - 5

The actual value of CT is chosen to make the C,a,,At term dimensionless. With this consideration, the GL equation form provisionally becomes:

CT, = eXp{- C~a&t[l+ 0.8C~a&). (C-5)

where At=(t-15.555556).

C.5.2

The second change is to directly use the metric base temperature T , not 60°F (IPTS-68). This goes beyond simply changing the units. We would like to directly use an expression using the new base temperature in the same general form of:

Shift of Base Temperature Value

where the constants 4 and B, may be different from the 1.0 and 0.8 used in the 60°F version of the CTL equation. For a consistent CTL correlation, the new set of coefficients 4 and B, must be related to the old constants of 1.0 and 0.8. Keeping units of OF fort and T temporarily the equation develops as follows:

- exp{ -a60( t -T) [1+0 .8a60{ ( t -T)+2(T-60) } ] } P

PT

This shows that we cannot use the customary unit form of the equation when we actually change the value of the base temperature because it now includes the 2(T - 60) term. However, this is a very small modification to the general equation form. So, a version of the general equation that can be used with a change in the base temperature is (t, T and 6r are in OC):

where 6, = 2(T - T60) and Go is 60°F (IPTS-68) in OC. This form is invariant with changes of base temperature and units on base temperature. Notice that no matter what base temperature is used, it is the 60°F (IPTS-68) values of 1.0,0.8, and a60 that are required in (C.8).



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c.5.3

The third required change involves how the a60 term is calculated. The equation form is Equation (C.2). The KO , Ki , and K, coefficients have been developed to be used with the base density at 60°F, p60. However, when we change the temperature base, even though we still need a60 , we will no longer be having p60 at Go , but rather p T at T (in OC). The mathematical manipulation to use p T instead of p60 (here, with no change of units) is:

Calculation of the 60°F Thermal Expansion Factor

where the modified coefficients KO,T and ( p T / &o)' and ( p T /&o), respectively. There is no simple ( p T / &o) relationship to convert the KO and Ki constants to corresponding KO,T and base temperature Go into equation C.8:

are related to the original coefficients KO and Ki by the ratios

constants. Substituting the metric base temperature T and the original

so now the correlation for a 6 0 in terms of p T is:

This is a non-linear expression in a60 so it cannot be solved explicitly for any arbitrary value of p T at T . Also, by virtue of how a60 is calculated from p60, the ratio ( p T / p60) is not constant for any range of p60. So, if KO and Ki are constants then the corresponding KO,T and are not.

While the KO,T and correlation for the metric base temperatures that could not be guaranteed to be consistent with the CTL expression for customary units.

values might be recorrelated as constants using p T , this Standard would then have a new

Therefore, it is not feasible to develop an equation for metric temperature bases in the form of equation C.11 that can be solved. The solution adopted for metric base temperatures in the revision of this Standard is to first compute densities at 60°F, in accordance with the data base developed for the 1980 Tables, using an iterative approach as described in Appendix F

C.6 Conversion to ITS80 Temperature Scale

The manipulations shown above do not include corrections needed to change from the IPTS-68 temperature scale to the ITS-90 temperature scale. Implementation of the ITS-90 temperature scale posed problems of a shift in the base temperature similar to those discussed for metric base temperatures. When converting the 60°F equations for use with the ITS-90 temperature scale, the base temperature is no longer the original IPTS-68 60°F but a slightly different value, t, , approximately 60.007"F. The shift factor required for use in the equation form of (C.8) will be:

6, 2(t, -60) = 0.01374979547. (C.12)



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Because the temperature shift is so small, iterative equations can be applied in a very simple manner to get a pm

that is consistent with IPTS-68, given a pm consistent with ITS-90. This means that the a60 value can easily be calculated and the equations for the shifted base temperature used in this Standard.

For computations involving the customary base temperature of 60°F, the procedure that has been adopted is to shift the input temperature and the input p60, if given, to an IPTS-68 basis. If pmis not given, a value is calculated using an iterative procedure and this is then shifted to an IPTS-68 basis. The calculation of C , involves IPTS-68 values of pm , while At is the temperature differential expressed on the IPTS-68 scale.

For metric base temperatures, all relevant temperatures (base, observed and alternate) are first converted from "C to OF, where both units are expressed on the temperature scale ITS-90. If given, the p T value (where T is the metric base temperature) is used to calculate p60 (ITS-90). The procedure then follows that described above for the 60°F system, with temperatures and base density shifted to IPTS-68.

Since the procedures for the customary and metric base systems utilize the same routines, they deliver identical results when starting from equivalent input values.



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i

Appendix D - International Temperature Scale of 1990, ITS-90

ai i ai

Changes to the International Temperature Scale Since 1980

1 2 3 4

The International Committee for Weights and Measures, CIPM, publishes the international temperature scale. Its purpose is to define procedures by which specified practical thermometers of the required quality can be calibrated in such a way that the values of temperature obtained from them can be precise and reproducible while at the same time closely approximating the corresponding thermodynamic values. Small amendments to the temperature scale are introduced from time to time by CIPM to improve precision and reproducibility and provide better continuity between sections of the scale.

-0.148759 5 -4.089591 -0.267408 6 -1.871251 1 .O80760 7 7.438081 1.269056 8 -3.536296

Since the international temperature scale is used for the calibration of thermometers, the values of temperature- dependent physical parameters of materials will, in principle, depend on what scale is in force at the time the parameter is measured or referenced. However, since changes between scales are relatively small, this effect will only become noticeable at high levels of precision.

When the 1980 Petroleum Measurement Tables were prepared, the temperature scale in effect was the International Practical Temperature Scale of 1968 (IPTS-68). The International Temperature Scale of 1990 (ITS-90) superseded this in 1990.

When the 1980 Petroleum Measurement Tables were prepared, the temperature scale in effect was the International Practical Temperature Scale of 1968 (IPTS-68). The International Temperature Scale of 1990 (ITS-90) superseded this in 1990. The developers of ITS-90 fitted the differences between the ITS-90 and IPTS-68 temperature scales to an 8* order polynomial of the form:

Note that this polynomial is useful over the range of -200°C to 630°C.

The following figure shows the magnitude of the differences between the ITS-90 and equivalent IPTS-68 temperature values in the range of this Standard. Over this temperature range, the differences in the two temperature scales are no larger than 0.04"C (0.07"F).



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0.02 1

0.01 Y 2 0.00 U

4 O

B -Omo1 '1 3 -0.02 8 S g! -0.03

-0.04

-0.05 ' -250 -200 -150 -100 -50 O 50 100 150 200 250

ITS-90 Temperature (b,90) (OC)

Impact on the Petroleum Measurement Tables

The principal physical parameter contained in the Petroleum Measurement Tables that is affected by the change from IPTS-68 to ITS-90 is density and the related properties of relative density and API gravity.

Values of the density of a substance are a function of its temperature. For petroleum hydrocarbons, the Petroleum Measurement Tables are based on average relationships between density and temperature according to broad classifications of products. The precision of the VCF values, which represent the change of density with temperature, is to 5 decimal places.

The changes due to ITS-90 give differences at high temperatures of no more than kO.00003. Even though this is well within the inherent accuracy of the correlations, because this would be noticeable, it was decided to fully incorporate procedures to account for differences between ITS-90and IPTS-68. Converting the input ITS-90 temperatures to equivalent IPTS-68 values before making any calculations in 1 1.1.6.1 did this.

One other subtle effect of the temperature scale correction is that the customary standard temperature, 60°F, has undergone a slight shift. What is 60°F in ITS-90 is an equivalent 60.00687490"F in IPTS-68. Because of this, any input 60°F standard density values must be corrected to an equivalent IPTS-68 60°F value, before the value can be usedin the am and Fp correlations.

60°F Water Density

Another parameter in the Tables that is affected by the change of temperature scale is the density of water at 60°F, which affects the relative density and API gravity. While density is a simple physical property (the mass of a substances divided by its volume at a specified temperature), calculations of relative density and API gravity relate to the density of water as well as the density of the hydrocarbon. Since pure water is a defined substance, it has different density values on IPTS-68 and ITS-90 dependent on the temperature of the measurement. In addition, a new, more accurate equation of state has been adopted for giving water densities. The value at 60°F (ITS-90) has been re-defined as 999.016 kg/m3 for air-free water, based on new laboratory work by Patterson & Morris



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(Metrologia, 1994,31,277-288). The value used in the 1980 Tables was 999.012 kg/m3 (0.999012 g / d ) based on earlier laboratory work and applying IPTS-68.

The water density value of 999.016 kg/m3 at 60°F has been adopted for use in any conversion between density and relative density or API gravity.



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Appendix E - Development of Thermal Expansion Regression Equations

The correlations for the 60°F thermal expansion factor give results for an “average” liquid of a specific commodity type. However, there may be occasions when one wants to make density measurements on a particular liquid in order to determine its actual a60 value. The following is a development of the equations given in 11.1.5.2 as the procedure to determine the thermal expansion factor from a set of measured density data.

The p60 and a60 values must be determined from a set of density measurements using non-linear regression. In general, this would involve doing a two-variable minimization process. However, because of the form of the equations used to relate density to the thermal expansion factor, the process can be simplified to the solution of a single 3d order polynomial.

The goal of this regression is to determine p60 and a60 values so that some measure of the difference between the measured density values and values estimated from the CTL equation is minimized. Mathematically, we can express the function that represents this difference using the least squares criteria:

where there are N measured density values, pm,i is the i-th measured density value, and pi is the estimate of the density using the corresponding temperature of the i-th measurement. The function y is the “objective” function, the sum of the squared residuals. (All subsequent summations will not show the limits on the summation, but they remain 1 to N .) This objective function has the following features:

0 Since all terms are squared, each term in y is positive. Negative errors will add to and not cancel out positive errors.

0 If this objective function is at an unconstrained minimum, then the lSt derivatives with respect to each variable will be zero and all of the 2nd partial derivatives will be positive.

The equation relating density and temperature is:

where p is the density at O psig and any valid temperature, is the density at the base temperature 60°F, a 6 0 is the 60°F thermal expansion coefficient , At is the difference between the alternate temperature and the 60°F base temperature, and 6, is the base temperature shift factor (0.01374979547’F). The temperatures used to calculate At must be adjusted using the procedure in 11.1.5.3 and the value for the base temperature should also be shifted consistent with 1 1.1.5.3,60.0068749”F. Using Equation (E.2) the objective function can be expressed as:

y=-C(lnp,,, 1 -lnp, +amAt, [1+0.8a,(Ati +6,)])2

= -E( 1 ln p,,, - ln p, + a,At + 0 . 8 ~ ~ ; ( At,) ( Ati + 6 T ) ) 2

2

2

This expression can be fully expanded to:



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The various summations in Equation (E.4) need only be calculated once and then be treated as constants when adjusting the p60 and a60 values. Equation (E.4) can be restated as:

1 1 2 2

?=-s,, -inp,s, +-(lnp,)’ N+a,S,

+0.8a;6,SfP -am ln pmSf - 0.8ab6, lnp,S,

+-a;Sn + 0.8ai06,Sn + 0.32ak6;Sn + 0.8a;S&

-0.8a; ln pmSn + 0.8a&Sm + 0.64ak6,Sm + 0.32a&Sm

1 2

with the following definitions of the variables to represent the summations:

s p Clnpm,i

S, = CAt i

Sip = C Ati . lnpm,i

S, = C(Ati)’ (E-10)

S,,, = C(Ati)’ -lnpm,i (E-11)

S, = C(Ati)3 (E.12)

S, = C(Ati)4 (E. 13)

In the data fitting process, the two adjustable variables are p60 and a60. An unconstrained minimum will be at an extremum point, Le., a point where each lSt derivative with respect to a variable is zero. The lSt derivatives for these variables are:

(E-14) = -(-Sp 1 +lnp,N-a& -0.8a;6,Sf -0.8a&Sn)

P60

and:



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= S,, + 1 .6a,6,Sf, - ln p,S, - 1.6a,6, ln p,S, + a,&

+2.4a;6,Sn +1.28a&6&S, +1.6a,S,, -1.6a, lnp,S,

+2.4a;S, + 2.56a&6,Sm + 1.28a&Sm

(E. 15)

Denote the values of the two adjustable variables at the extremum point as p* and a*. These values are solutions to the two simultaneous equations resulting when setting the lSt derivatives equal to zero:

O=-S,+lnp*N-a*S, -0.8(Sn +660Sf)a*2 (E. 16)

and:

O = S,, + 1 .6a*6,Sfp - ln p*S, - 1.6a*6, ln p*S, + a*S,

+2.4aY6,S, + 1 .28a*36&S, + 1.6a*S,, - 1.6a* ln p*Sn

+2.4aYS, + 2.56a*3660S, + 1.28a*3Sm

(E. 17)

Both equations are non-linear with respect to a* but the first equation gives a direct relationship between the optimal values of p* and a* :

a*2 * S, S, * O.8(S,+6,Sf) lnp =-+-a +

N N N

This can be substituted into Equation (E.17) to give a single non-linear equation in a:, :

S: +1.6(Sn +6,S,)S, N

O = [ S,, -%] + [S , + 1.6( S,,, + 6,Sfp) -

Notice that (E.19) is just a 3d order polynomial equation in a:, :

O = a, + ala:, + a,azz + a3az$

with the coefficients defined from:

S: +1.6(S, +6,S,)S, N

a, =S,+1.6(Sn,+6,Sfp)-

N

(E. 19)

(E.20)

(E.21)

(E.22)

(E.23)



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(E.24)

The equation leading to a* is a cubic and there is a procedure to determine its roots analytically. However, this procedure is fairly complex. Sometimes it is simpler to use a numerical method (such as Newton’s method) to determine the numerical values of the roots. A Newton’s iteration method with the following steps is used in 11.1.5.2:

1. Initialize the value for a* . The result from a linear regression of lnp, vs. At with 6, = O is used as the initial guess:

2. Determine the “residual” for this guess:

f = ao +ala* + a2a*2 + a3a *3

3. Determine the derivative of the residual for this guess:

f ’ = a, + 2a2a* + 3 ~ , a * ~

4. Determine a correction to this guess:

5. Update the value for a* :

a* t a * +Aa*

6. Return to step 2 until some convergence criteria is achieved. Some convergence criteria are small values of the residual, small values of the update value, andíor a set number of iterations.

Since the equation leading to a* is a cubic, it is guaranteed to always have at least one real root, but may have two or three. Because the coefficients are generated from expressions that involve sums and differences of (mostly) positive summations, we cannot tell apriori the signs of the coefficients and how many positive real roots we will have. From geometric considerations, we will have the following:

0 The objective function surface should be a quartic function in the plane of the ln p* value(s) and a

quadratic in the plane of the a* values. Both of these should be concave down.

0 If there are multiple roots to the cubic equation giving the a* value, two of the roots should be associated with local minima & the third with a local maximum. The root associated with the local maximum should lie between the two roots associated with the local minima.



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Appendix F - Development of Iteration Equations

The basic iteration scheme to determine the 60°F base density p60 from the observed density po is outlined in 11.1.3.5. It is pointed out that a Newton's method defines a specific way to calculate a new p60 estimate from the previous estimate. In this appendix the actual equations used for the Newton's methods will be developed.

In the following equations variables that may change from one iterative step to the next will be denoted with a superscript '(m)' where the m denotes the m-th iterative step. For example, the value of p60 used on the first iterative step will be the value used on the second iterative step will be ~ ( 6 2 0 ) ~ and so on.

Newton's Method

Newton's method gives a procedure for finding a numerical value for the zero of a function, Le., for a function f(x) finding a specific value of X such that f ( X ) = O. The function f ( x ) is approximated as a straight-line about a point xo ; this approximate equation can then be solved for X . Using a little bit of calculus, the function f ( x ) can be exactly expanded as a Taylor series polynomial:

(x - x0)" f'"' (xo ) + f - n!

where the derivatives are evaluated at the point x = xo . The approximate straight-line equation is obtained by dropping all terms after the first derivative:

f ( 4 = f (xo)+(x-xo) f ' (xo) . F-2)

Remembering that X is defined as the point where the function's value is zero, we can solve this approximate equation for X :

F-3) f(X)=o=f(xo)+(x-xo)f'(xo) - X=x, --. f (xo 1 f l x 0

If we expand the function about each iterative value then x ( m ) plays the role of xo and the next iteration's value x(m+l) plays the role of X . The recursion formula becomes:

Two notation changes can be made: the function and derivative values may be denoted with the iteration's superscript ( f ( m ) and f ' ( m ) instead of f ( x ( m ) ) and f ' ( x ( m ) ) ) and the ratio of the function to its derivative can be referred to as the step change, h ( m ) . So, this recursion formula can also be expressed as:

f (m) Y(") . F-5) x(m+l) = x ( m ) + h ( m ) where h ( m ) E --

Derivation of This Standard's Newton's Method Equations

The Newton's method iteration procedure to find &o given an observed p is:



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SECTION 1 - VOLUME CORRECTION FACTORS FOR CRUDE OILS, REFINED PRODUCTS, & LUBE OILS

where the step change Apg) is calculated from:

218

DF' = Dr'a',"'At [ 1 + 1.6a',"' (At + 6, )] (F-9)

2Cg)PF9)(7.93920 + 0.02326t) (F. 1 O) = -

P P 2

These recursion equations can be developed by starting with the residual function:

f ( P 6 0 ) = cTPL 'P6O -P= 'TL .cPL 'P60 -P (F. 1 1)

(where f ( ~ 6 0 ) = O corresponds to the solution). The Newton's method recursion equation will come from:

where:

(F.12)

(F. 13)

Using this definition for the residual function and its derivative, the iteration scheme can be expressed as:

(F.14)

We can change the appearance by dividing the numerator and denominator by @)CE) and factoring out a -1 from the numerator (changing the order of the subtraction):

We can simplie the looks of equation (F. 15) by defining two derivative terms:

(F. 15)

(F. 16)

(F. 17)

SO:



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(F. 18)

The various derivatives can be determined fiom the basic equations. Neglecting any differences between the ITS-90 and IPTS-68 temperature scale densities (i.e..y dp,/dp* = 1 ), the CTL expressions:

C, =exp(-a,At[1+0.8a,(At+6,)]) (F. 19)

K,+K,P*+K,P*~ KO KI am = =?+*+K2 P*, P P

give the derivatives:

= -C, (At [i +1.6a, (At +6,)]) ab dP60

The CPL expressions:

1 1 - 10-5 F,P CPL =

793920+2326t P* 1 -1.9947+0.000134270t+

give the derivatives:

FI--- dFP ( 79392;; 2326t 793920 + 2326t dFp y = -2F P - dP6Q dP

SO DY) is:

(F.20)

(F.21)

(F.22)

(F.23)

(F.24)

(F.25)

(F.26)

(F.27)

(F.28)

Note that the derivative terms do not have to be extremely accurate since they only establish the magnitude of the change fiom one iteration to the next. If they values are offy usually one extra iteration is needed to achieve convergence. That is why we can interchange the pm and pio values in these derivative terms.



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0.0009

0.0008

0.0007

dn 0.0006 LL u 0.0005 O

al 3 - >m 0.0004 O a" 0.0003 0.0002

0.0001

0.0000

Simplification of the Temperature Derivative Term

Let's go back to the manipulation can be made simplie the calculation. Equation (F.23) can be modified to:

term in Equation (F.23). The a60 derivative could be replaced with Equation (F.24), but a

10.0

-: !- 9.0 9 Function Value @ Dimensionless Derivative !- 8.0 -:

!- 7.0 O

!- 6.0 0 -! e

!- 5.0 O -I P -I

-! a"

e

:- 4.0 II

;- 3.0 !- 2.0

-: !- 1.0

0.0

-I

" " " " ' ~ " " " " ' ~ " ' " " " ~ ' " " " " ~ " " " " ' ~ " " " ' " ~ ' " " " " ~ " " " " ' ~ " " " " ' ~ " " ' " " ~ " ' " " "-

(m)

DT = -p,At[l+l.6a',"'(At+6,)][~~&] = ~~' ,")At[1+1.6~~' ,") (At+6~)]

(m)

DT =a',"'At[1+1.6a',"'(At+6,)] [ - &] = a',")At(1+1.6a',"'At)[Dp)] (F.29)

where the term in the square brackets is the dimensionless a 6 0 derivative and is designated as 0,. The expression for Da is:

Da = 2K0 + Kip* 2Ko +KIP, KO + Kip* + K2py KO + Klp, + K2pk

(F.30)

This definition is convenient because of the nature of D, for the Equation (F.20) for a 6 0 . Depending upon the values of KO , KI , and K2 , the 0, values are constant or are nearly constant. For example, for the Generalized Crude Oils, KI = K2 = O , so Da = 2 for all p, values. Similarly, for the Generalized Lubricating Oils, KO = K2 = O , so Da = 1 for all p, values. For nearly all of the commodity groups the 0, values are or are nearly constant, but different, values. The only exception is the Transition Zone (770.3554 < p60 < 787.5224) where there is a significant change in the value (see the following figure) -however, a constant value of 8.5 does not significantly harm the convergence properties of the iteration equation.

Refined Product CL Correlations

Using the approximate constant 0, values for the different commodity groups, the DT term becomes:



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Crude Oil

Fuel Oils

DF' = D?'a',"'At [ 1 + 1.6a',"' (At + 6, )] . (F.30)

Density Range(kg/m3) Da 610.6 < p60 < 1163.5 2.0

1.3 838.3154 < p60 < 1163.5

This equation shows Da changing with the iterations; however, as long as the commodity group does not change during the iterations, this would actually be a constant.

The following table shows the appropriate Da to use for the various commodity groups.

Jet Fuels

Transition Zone

Gasolines

Lubricating Oil

Special Applications

787.5224 < < 838.3 154 2.0

770.3554 < p60 < 787.5224 8.5

610.6 < < 770.3554 1.5

1 .o 800.9 < p60 < 1163.5

All p60 values 0.0

Special Applications - "C" Tables

What happens to the iteration equations if the a60 value is not calculated from the correlations but instead is pre- calculated and specified? The need for iteration is reduced. In fact, if no pressure correction is applied, the need for iteration could be eliminated entirely.

Equation (F.29) gives the DT factor in the recursion formula. If the a 6 0 value is specified then it does not change with the p60 values and ak0 = O , leading to Da = O and D P ) = O. This simplifies the recursion formula Equation (F.18) to:

(F.3 1)

When a pressure correction is applied iterations will be needed since the D Y ) term is not necessarily zero. However, if no pressure correction is applied, then the p60 value could be directly calculated, or, keeping the iteration procedure, only one iteration need be done. When no pressure correction is applied, C,, = 1 , and D Y ) = O , leading to:

(F.32)

When a60 is specified, CTL is not a function of p60 and will not change from one iteration to the next. For any estimate, only one Newton step is necessary to find the correct value of p60.

Use of Iteration Equations to Shift 60°F Standard Density

The Newton's Method equations developed here have been used to develop the equation in 11.1.6.1 to shift pm to

p* for subsequent use in the equations to calculate am and Fp . This was easy to accomplish since the temperature difference between p* is very small. When done as an iterative procedure, only one iteration is ever needed. Since only a single iteration is needed, the specific starting values can be put into the iteration equations and it can be recast as a single equation to shift the pm value to p* .



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The shift equation can be most easily developed using the equations based upon the IPTS-68 60°F value being the standard temperature and the ITS-90 60°F value (to be denoted as t , ) as the alternate temperature. The initial

estimate to the IPTS-68 60°F density, p* , will be the given ITS-90 60°F density, p60. Starting with (F.18):

(F.33)

Since the IPTS-68 60°F value is being used as the standard temperature (F. 19) becomes:

Cg) = exp ( [ -aE)At 1 + O.da"At]) = exp (-a:) ( t , - 60) [ 1 + 0.8az) ( t , - 6O)]) (F.34)

where a:) is calculated using p60 in (F.20):

(F.35)

Or) is calculated using p60 in (F.9):

0;) = @')a:) ( T, - 60) [ 1 + 1.6~~:) ( T, - 6O)] (F.36)

and Dao) is calculated using p, in (F.30):

(F.37)

The temperature difference ( t , - 60) is based upon the IPTS-68 values for temperature and is used to define the

value of 6, ; specifically, it is %6,. Combining this with (F.34), (F.36), and (F.37) changes (F.33) to:

exp [ 0.5ag6, (i + O.4ag6,)I - i 1+

1 + 0.5ag6, (1 + 0.8az)6,

Finally, making the following symbolic substitutions:

A = 0.5ag6, = $[(:+KI)-& + K2]

the form for the final shift equation has been developed:

exp [ A( 1 + 0.8A)I - 1 1 + A( 1 + 1.6A) B

(F.38)

(F.39)

(F.40)

(F.41)



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